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Mathematical formula
single-digit remains, which is called the multiplicative digital root of n {\displaystyle n} . The multiplicative digital root for the first few positive integers
Multiplicative_digital_root
Repeated sum of a number's digits
The digital root (also repeated digital sum) of a natural number in a given radix is the (single digit) value obtained by an iterative process of summing
Digital_root
Figurate number
by a 0 or 5; a final 8 must be preceded by a 2 or 7. In base 10, the digital root of a nonzero triangular number is always 1, 3, 6, or 9. Hence, every
Triangular_number
Property of a number
is the smallest number of multiplicative persistence 3. In base 10, there is thought to be no number with a multiplicative persistence greater than 11;
Persistence_of_a_number
Numbers obtained by adding the two previous ones
includes as a subproblem a special instance of the problem of finding the multiplicative order of a modular integer or of an element in a finite field. However
Fibonacci_sequence
Number raised to the third power
perfect cubes must have digital root 1, 8 or 9. That is their values modulo 9 may be only 0, 1, and 8. Moreover, the digital root of any number's cube can
Cube_(algebra)
Number divisible only by 1 and itself
from the multiplicative group of the field to a totally ordered additive group, also called orders), absolute values (certain multiplicative mappings
Prime_number
Number equal to the sum of its proper divisors
until a single digit (called the digital root) is obtained, always produces the number 1. For example, the digital root of 8128 is 1, because 8 + 1 + 2
Perfect_number
Prime number of the form 2^n – 1
congruent to 7 mod 8, so 2 is a quadratic residue mod 2p + 1, and the multiplicative order of 2 mod 2p + 1 must divide ( 2 p + 1 ) − 1 2 = p {\textstyle
Mersenne_prime
Function whose domain is the positive integers
f is multiplicative, then so is g. If f is completely multiplicative, then g is multiplicative, but may or may not be completely multiplicative. There
Arithmetic_function
Numbers with a certain property involving recursive summation
{\displaystyle b} that eventually reaches 1 when iterated over the perfect digital invariant function for p = 2 {\displaystyle p=2} . The origin of happy
Happy_number
Product of an integer with itself
a square each side of which has the same number of points as the square root of n; thus, square numbers are a type of figurate numbers (other examples
Square_number
Ten raised to an integer power
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Power_of_10
Arithmetic operation
invertible elements in a multiplicative monoid, that is, an algebraic structure, with an associative multiplication and a multiplicative identity denoted 1
Exponentiation
Type of composite number with an even number of digits
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Vampire_number
Sum of a number's digits
decimal digital root of any non-zero integer will be a number in the range 1 to 9, whereas the digit sum can take any value. Digit sums and digital roots
Digit_sum
Integer filtered out using a sieve similar to that of Eratosthenes
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Lucky_number
Recursive integer sequence
0 c ( x ) = 1 . {\displaystyle C_{0}=\lim _{x\to 0}c(x)=1\,.} The square root term can be expanded as a power series using the binomial series 1 − 1 −
Catalan_number
Class of natural numbers with many divisors
Ramanujan (1915). For example, the number with the most divisors per square root of the number itself is 12; this can be demonstrated using some highly composites
Superior highly composite number
Superior_highly_composite_number
Number that remains the same when its digits are reversed
number whose cube is a palindrome is 2201, and it is a conjecture the fourth root of all the palindrome fourth powers are a palindrome with 100000...000001
Palindromic_number
Iterative algorithm on numbers
Meertens number Narcissistic number Perfect digit-to-digit invariant Perfect digital invariant Sum-product number For six-digit numbers, i.e. n=6, (1) 6=3×2
Kaprekar's_routine
Two raised to an integer power
starting point 2k, and the period is the multiplicative order of 2 modulo 5k, which is φ(5k) = 4 × 5k−1 (see Multiplicative group of integers modulo n).[citation
Power_of_two
Integer having a non-trivial divisor
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Composite_number
Type of figurate number
Like a triangular number, the digital root in base 10 of a hexagonal number can only be 1, 3, 6, or 9. The digital root pattern, repeating every nine
Hexagonal_number
Positive integer of the form (2^(2^n))+1
multiply this by a number A, which is greater than the square root of P and is a primitive root modulo P (i.e., it is not a quadratic residue). Then take
Fermat_number
Number that is less than the sum of its proper divisors
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Abundant_number
Count of the possible partitions of a set
numbers, then B n {\displaystyle B_{n}} gives the number of different multiplicative partitions of N {\displaystyle N} . These are factorizations of N {\displaystyle
Bell_number
Numbers that evenly divide powers of 60
roots, such as how the Babylonians found an approximation to the square root of 2, perhaps using regular number approximations of fractions such as 17/12
Regular_number
Infinite integer series where the next number is the sum of the two preceding it
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Lucas_number
Numbers with many divisors
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Highly_composite_number
Power of a prime number
power excluding powers of 2 greater than 4 has a primitive root; thus the multiplicative group of integers modulo pn (that is, the group of units of
Prime_power
Number used for counting
arithmetical operations are defined on natural numbers: addition and multiplication. However, the inverse operations, subtraction and division, only sometimes
Natural_number
Numbers that contain only the digit 1
prime, and this n {\displaystyle n} value is r {\displaystyle r} itself or a root of r {\displaystyle r} ) b {\displaystyle b} is not in the form − 4 k 4 {\displaystyle
Repunit
Integers occurring in the coefficients of the Taylor series of 1/cosh t
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Euler_numbers
Number of stacked spheres in a pyramid
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Square_pyramidal_number
Integer having only small prime factors
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Smooth_number
Product of two prime numbers
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Semiprime
Polyhedral number representing a tetrahedron
4.[dubious – discuss] By analogy with the cube root of x, one can define the (real) tetrahedral root of x as the number n such that Ten = x: n = 3 x
Tetrahedral_number
Result of multiplying four instances of a number together
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Fourth_power
Type of number introduced by Mike Keith
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Keith_number
Number used to approximate the square root of 2
comprise the denominators of the closest rational approximations to the square root of 2. This sequence of approximations begins 1/1, 3/2, 7/5, 17/12
Pell_number
Pair of integers related by their divisors
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Amicable_numbers
Odd number with specific properties
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Sierpiński_number
Composite number in number theory
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Carmichael_number
Base-dependent property of integers
Inv ( a , c ) {\displaystyle \operatorname {Inv} (a,c)} denote the multiplicative inverse of a {\displaystyle a} modulo c {\displaystyle c} , namely the
Kaprekar_number
Figurate number
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Pentagonal_number
Number sequence 3,0,2,3,2,5,5,7,10,...
x − 1 = 0 {\displaystyle x^{3}-x-1=0} . If the three solutions are real root α {\displaystyle \alpha } (with approximate value 1.324718 and known
Perrin_number
Number of form 2^(2^p-1)-1 with prime exponent
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Double_Mersenne_number
Square of a triangular number
Row (1893) obtains another proof by summing the numbers in a square multiplication table in two different ways. The sum of the ith row is i times a triangular
Squared_triangular_number
Integer divisible by sum of its digits
one as follows: Inserting zeroes into N will not change the sequence of digital sums (just as 21, 201 and 2001 are all 10-harshad numbers). If we insert
Harshad_number
Size of a geometric arrangement of points
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Figurate_number
Number that cannot be written as an aliquot sum
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Untouchable_number
Number that is the result of operation on its own digits
numbers are a subset of Friedman numbers where the only operation is a multiplication of two numbers with the same number of digits, for example 1260 = 21
Friedman_number
Concept in number theory
In number theory, a narcissistic number (also known as a pluperfect digital invariant (PPDI), an Armstrong number (after Michael F. Armstrong) or a plus
Narcissistic_number
Type of Poulet number
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Super-Poulet_number
Type of composite integer
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Smith_number
Numbers k where x - phi(x) = k has many solutions
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Highly_cototient_number
Centered figurate number
10333, 10837, 11353, and 11881. (sequence A003154 in the OEIS) The digital root of a star number is always 1 or 4, and progresses in the sequence 1,
Star_number
Combinatorial sequence of numbers
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Dedekind_number
Three raised to an integer power
which is a power of two and much smaller. Power of 10 Power of two Square root of 3 Ranucci, Ernest R. (December 1968), "Tantalizing ternary", The Arithmetic
Power_of_three
Class of binary number
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Evil_number
Numbers whose prime factors all divide the number more than once
powerful numbers in the interval [1,x]. Then k(x) is proportional to the square root of x. More precisely, c x 1 / 2 − 3 x 1 / 3 ≤ k ( x ) ≤ c x 1 / 2 , c = ζ
Powerful_number
Number that represents a hexagon with a dot in the center
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Centered_hexagonal_number
Area of a right triangle with rational-numbered sides
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Congruent_number
Positive integer that is the product of three distinct prime numbers
number (except by 1) is not sphenic. This is easily provable by the multiplication process at a minimum adding another prime factor, or raising an existing
Sphenic_number
Number, product of consecutive integers
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Pronic_number
Integer whose representation contains every digit in its number base
square numbers. No pandigital cube and no pandigital number with an integer root of higher degree are known. For each natural number n, there exists a maximum
Pandigital_number
Numbers in a type of Lucas sequence
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Jacobsthal_number
Type of natural number
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Colossally_abundant_number
Numbers parameterizing ways to partition a set
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Mathematical concept
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Lucky_numbers_of_Euler
Integer whose multiples are digit rotations
specifically, this sequence is the set of primes p such that b is a primitive root modulo p. A conjecture of Emil Artin is that this sequence contains 37.395
Cyclic_number
Number of orderings allowing ties
2^{n-1}} ordered multiplicative partitions. Numbers that are neither squarefree nor prime powers have a number of ordered multiplicative partitions that
Ordered_Bell_number
Two or more natural numbers with a common abundancy index
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Friendly_number
Natural number with a decimal representation made of repeated instances of the same digit
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Repdigit
Number whose square ends in the same digits
root in roots: for i in range(0, base): new_i = i * base ** (power - 1) + root new_root = polynomial_function(new_i) % pow(base, power) if new_root ==
Automorphic_number
Integer describing itself
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Self-descriptive_number
Type of figurate number
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Polygonal_number
Natural number
generally, in algebra, it denotes the multiplicative identity in any unital ring or field. An element with a multiplicative inverse is called a unit, generalizing
1
Number, non-palindrome after repeated sum with reverse
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Lychrel_number
Positive integer whose divisors have a harmonic mean that is an integer
1997). All of the terms in this formula are multiplicative, so that the harmonic mean H(n) is also multiplicative. It follows that, for any positive integer
Harmonic_divisor_number
Integer named after Reo Fortune
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Fortunate_number
Type of positive integer
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Erdős–Woods_number
Mathematical sequences in combinatorics
so calculating a product entry involves an infinite sum, the matrix multiplications work because these matrices are lower triangular, so only a finite
Stirling_number
Sequence of integers
= 0. {\displaystyle x^{3}-x-1=0.\,} This equation has 3 roots; one real root p (known as the plastic ratio) and two complex conjugate roots q and r. Given
Padovan_sequence
Concept in combinatorics
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Cake_number
Numeral ambigram
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Strobogrammatic_number
Number of unique ways to draw non-intersecting chords in a circle
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Motzkin_number
Abundant number whose proper divisors are all deficient numbers
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Primitive_abundant_number
Integer that is both a perfect square and a triangular number
all integers from 1 {\displaystyle 1} to n {\displaystyle n} has a square root that is an integer. There are infinitely many square triangular numbers;
Square_triangular_number
Number equal to the sum of all or some of its divisors
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Semiperfect_number
Concatenation of the first n prime numbers
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Smarandache–Wellin_number
Number whose divisors summed twice over equal twice itself
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Superperfect_number
Number that when multiplied by another number moves its last digit to its front
{k}{10n-1}}(10^{m}-1)} where m is the length of the period; i.e. the multiplicative order of 10 modulo (10n − 1). For another example, if n = 2, then 10n
Parasitic_number
Type of pseudoprime
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Frobenius_pseudoprime
Numbers whose sum of divisors is twice the number plus 1
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Quasiperfect_number
Algorithms for calculating square roots
costly than multiplication, it may be preferable to compute the inverse square root instead. Other methods are available to compute the square root digit by
Square_root_algorithms
Number whose first n digits is a multiple of n
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Polydivisible_number
Positive integer that is an integer power of another positive integer
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Perfect_power
Positive integers with specific properties
Persistence Additive Multiplicative Digit sum Digit sum Digital root Self Sum-product Digit product Multiplicative digital root Sum-product Coding-related
Noncototient
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
Girl/Female
Bengali, Gujarati, Hindu, Indian, Malayalam, Sanskrit
Progressive; A Digit of the Moon
Surname or Lastname
English
English : variant of Roots.
Boy/Male
Indian, Sanskrit
Regent of a Direction
Girl/Female
Hindu
Digit of the Moon
Boy/Male
Indian, Sanskrit
Digit of the Moon
Boy/Male
Indian, Sanskrit
Inflamed
Girl/Female
Hindu, Indian
Giving Honour; A Digit of the Moon
Boy/Male
Indian, Punjabi, Sikh
Protector of All Directions
Girl/Female
Gujarati, Hindu, Indian
Expert; Splendor; Name of Parvati
Female
Hebrew
(מֵרַב) Variant spelling of Hebrew Merab, MERAV means "increase, multiplication."Â
Female
Hebrew
(מֵרַב) Variant spelling of Hebrew Merav, MERAB means "increase, multiplication." In the bible, this is the name of the eldest daughter of King Saul.Â
Girl/Female
Tamil
Divine power
Girl/Female
Hindu, Indian, Tamil
Light; Chamak
Girl/Female
Indian
Moon Rays
Girl/Female
Indian
Divine power
Girl/Female
Tamil
Dixita | திகà¯à®·à®¿à®¤
The right path
Dixita | திகà¯à®·à®¿à®¤
Surname or Lastname
English
English : patronymic from Root 1.
Girl/Female
Indian
Light
Girl/Female
Tamil
Indukala | இஂதà¯à®•à®²à®¾
Digit of the Moon
Indukala | இஂதà¯à®•à®²à®¾
Girl/Female
Indian
The right path
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
Boy/Male
Hindu, Indian
Controller of Destiny
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi
Who has No Enemies
Surname or Lastname
English
English : habitational name from Milby in North Yorkshire, named in Old Norse as ‘Mildi’s homestead’, from the personal name Mildi + býr ‘homestead’, ‘village’ (Old Danish by).
Girl/Female
Muslim/Islamic
Morning light
Girl/Female
Arabic, Muslim
Smile
Girl/Female
Muslim/Islamic
Pretty very beautiful
Boy/Male
Indian, Punjabi, Sikh
Glorious Friend
Girl/Female
Indian, Malayalam
Happines
Boy/Male
Gujarati, Hindu, Indian
Belonging to the Gods
Boy/Male
Indian
Renowned warrior
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
MULTIPLICATIVE DIGITAL-ROOT
adv.
So as to multiply.
a.
Tending to multiply; having the power to multiply, or incease numbers.
n.
The act or process of multiplying, or of increasing in number; the state of being multiplied; as, the multiplication of the human species by natural generation.
a.
Consisting of many, or of more than one; multiple; multifold.
n.
The art of increasing gold or silver by magic, -- attributed formerly to the alchemists.
a.
Remote from the point of attachment or origin; as, the distal end of a bone or muscle
n.
One twelfth part of the diameter of the sun or moon; -- a term used to express the quantity of an eclipse; as, an eclipse of eight digits is one which hides two thirds of the diameter of the disk.
n.
The result of any process inverse to multiplication. See the Note under Multiplication.
n.
An increase above the normal number of parts, especially of petals; augmentation.
n.
Formation into, or multiplication of, vacuoles.
n.
The dried leaves of the purple foxglove (Digitalis purpurea), used in heart disease, disturbance of the circulation, etc.
n.
Any one of several extracts of foxglove (Digitalis), as the "French extract," the "German extract," etc., which differ among themselves in composition and properties.
n.
Multiplication or increase by gemmation or budding.
a.
Pertaining to that which is distal; as, the distal tuberosities of a bone.
a.
Having leaflets like fingers; digitate.
a.
Characterized by polysyndeton, or the multiplication of conjunctions.
adv.
Toward a distal part; on the distal side of; distally.
n.
Superabundant fecundity or multiplication of the species.
a.
Of or performance to the fingers, or to digits; done with the fingers; as, digital compression; digital examination.
n.
The process of repeating, or adding to itself, any given number or quantity a certain number of times; commonly, the process of ascertaining by a briefer computation the result of such repeated additions; also, the rule by which the operation is performed; -- the reverse of division.