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Type of figurate number constructed by combining heptagons
mathematics, a heptagonal number is a figurate number that is constructed by combining heptagons with ascending size. The n-th heptagonal number is given by
Heptagonal_number
Centered figurate number that represents a heptagon with a dot in the center
other dots surrounding the center dot in successive heptagonal layers. The centered heptagonal number for n is given by the formula 7 n 2 − 7 n + 2 2 {\displaystyle
Centered_heptagonal_number
Natural number
heptagonal number. 1926 = 2 × 32 × 107. It is a pentagonal number. 1931 is a Sophie Germain prime. 1933 is a prime number and a centered heptagonal number
1000_(number)
Natural number
6000 (six thousand) is the natural number following 5999 and preceding 6001. 6028 – centered heptagonal number 6037 – super-prime 6047 – safe prime 6053
6000_(number)
Natural number
442 7246 – centered heptagonal number 7247 – safe prime 7260 – triangular number 7267 – decagonal number 7272 – Kaprekar number 7283 – super-prime 7291
7000_(number)
Figurate number
the nth m-gonal number and the nth (m + 1)-gonal number is the (n − 1)th triangular number. For example, the sixth heptagonal number (81) minus the sixth
Triangular_number
Shape with seven sides
regular heptagon. Apart from the heptagonal prism and heptagonal antiprism, no convex polyhedron made entirely out of regular polygons contains a heptagon as
Heptagon
Natural number
an emirp and more generally a permutable prime. 71 is a centered heptagonal number. It is a regular prime, a Ramanujan prime, a Higgs prime, and a good
71_(number)
Natural number
2273 – Sophie Germain prime 2276 _ centered heptagonal number 2278 – triangular number 2281 – star number, 2287 – balanced prime 2299 – member of a Ruth–Aaron
2000_(number)
Natural number
narcissistic number as 84 + 24 + 04 + 84 = 8208 8219 – twin prime with 8221 8221 – super-prime, twin prime with 8219 8233 – super-prime, centered heptagonal number
8000_(number)
Natural number
– pronic number 4166 – centered heptagonal number 4167 = 7! − 6! − 5! − 4! − 3! − 2! − 1!, number of planar partitions of 14 4169 – a number of points
4000_(number)
Natural number
octagonal number, dodecagonal number 3037 – star number, cousin prime with 3041 3046 – centered heptagonal number 3052 – decagonal number 3059 – centered
3000_(number)
Natural number
natural number following 105 and preceding 107. 106 is a centered pentagonal number, a centered heptagonal number, and a regular 19-gonal number. There
106_(number)
Natural number
167. It is a Motzkin number. 837 = 33 × 31. It is the 36th generalized heptagonal number. 838 = 2 × 419. It is a palindromic number. There are 838 distinct
800_(number)
Natural number
movement in Myanmar 970 = 2 × 5 × 97. It is a sphenic number and a heptagonal number. 971 is a prime number, an emirp, a Chen prime, and an Eisenstein prime
900_(number)
Natural number
triangular number 5167 – Leonardo prime, cuban prime of the form x = y + 1 5171 – Sophie Germain prime 5188 – centered heptagonal number 5189 – super-prime
5000_(number)
Natural number
22 × 33 × 5. It is a largely composite number, an untouchable number, a heptagonal number, and a decagonal number. It is the sum of a pair of twin primes
500_(number)
Natural number
perfect totient number like all powers of three. a heptagonal number. an icosioctagonal number. a centered octagonal number. a tribonacci number. an open meandric
81_(number)
Natural number
N. J. A. (ed.). "Sequence A128919 (Numbers simultaneously heptagonal and centered heptagonal)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation
148_(number)
Natural number
number. 316 = 22 × 79. It is a centered triangular number, a centered heptagonal number, an Ulam number, and a member of one Tetranacci sequence. It appears
300_(number)
Natural number
centered heptagonal number, a happy number, a Harshad number, and a nice Friedman number since 736 = 7 + 36. 737 = 11 × 67. It is a palindromic number and
700_(number)
Natural number
is a Markov number. 34 is also the fourth heptagonal number, and the first non-trivial centered hendecagonal (11-gonal) number. This number is also the
34_(number)
Natural number
decagonal number and a zero of the Mertens function. 638 = 2 × 11 × 29. It is a sphenic number, a nontotient, a centered heptagonal number, and the sum
600_(number)
Natural number
a sphenic number, a nontotient and a Harshad number. There are 402 graphs with 8 nodes and 9 edges. 403 = 13 × 31. It is a heptagonal number, a zero of
400_(number)
Natural number
of the first two of these). 616 is a polygonal number in four different ways: it is a heptagonal number, as well as 13-, 31- and 104-gonal. It is also
616_(number)
Natural number
– centered heptagonal number 9293 – Sophie Germain prime, super-prime 9316 – triangular number 9319 – super-prime 9334 – nonagonal number 9349 – Lucas
9000_(number)
Natural number
+ 23 + 29 + 31 + 37 197 is a centered heptagonal number, a centered figurate number that represents a heptagon with a dot in the center and all other
197_(number)
Natural number
amount of digits the 22nd triangular number. a star number. a centered heptagonal number. a centered nonagonal number. a Blum integer. a member of the 13-aliquot
253_(number)
Natural number
eighty-nine) is the natural number following 188 and preceding 190. 189 is a centered cube number and a heptagonal number. The centered cube numbers are
189_(number)
Natural number
preceding 236. 235 is a heptagonal number, a centered triangular number, and a Smarandache–Wellin number. It is a Harshad number in bases 6, 47, 48, 95
235_(number)
Natural number
twelve) is the natural number following 111 and preceding 113. 112 is an abundant number, a heptagonal number, and a Harshad number. There are 112 connected
112_(number)
Natural number
and a Harshad number in bases 2, 3, 4, 5, 6, 7, 8, 10, 13, 14 and 16 10009 = twin prime with 10007 10018 = centered heptagonal number 10080 = 21st highly
10,000
Natural number
number. Seven is the lowest natural number that cannot be represented as the sum of the squares of three integers. A seven-sided shape is a heptagon.
7
Figurate number
946, 1222, 1547, 1925 (sequence A002412 in the OEIS). The first few heptagonal pyramidal numbers are: 1, 8, 26, 60, 115, 196, 308, 456, 645, 880, 1166
Pyramidal_number
Number used for counting
natural-number results: subtracting a larger natural number from a smaller one results in a negative number and dividing one natural number by another
Natural_number
Polygonal number Triangular number Square number Pentagonal number Hexagonal number Heptagonal number Octagonal number Nonagonal number Decagonal number Centered
List of recreational number theory topics
List_of_recreational_number_theory_topics
Number divisible only by 1 and itself
A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers. A natural number greater than 1 that
Prime_number
Number equal to the sum of its proper divisors
In number theory, a perfect number is a positive integer that is equal to the sum of its positive proper divisors, that is, divisors excluding the number
Perfect_number
Natural number
palindromic number and a repdigit in base 2 (1111111112). It is also palindromic and a repdigit in base 8 (7778). It is a generalized heptagonal number (sequence
511_(number)
Product of an integer with itself
In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with
Square_number
Integer having a non-trivial divisor
A composite number is a positive integer that can be formed by multiplying two smaller positive integers. Accordingly, it is a positive integer that has
Composite_number
Natural number
lifetime of 73.8 calendar years. 27405 = heptagonal number, hexadecagonal number, 48-gonal number, 80-gonal number, smallest integer that is polygonal in
20,000
Odd number with specific properties
In number theory, a Sierpiński number is an odd natural number k such that k × 2 n + 1 {\displaystyle k\times 2^{n}+1} is composite for all natural numbers
Sierpiński_number
Numbers obtained by adding the two previous ones
month, the number of pairs of rabbits is equal to the number of mature pairs (that is, the number of pairs in month n – 2) plus the number of pairs alive
Fibonacci_sequence
Two raised to an integer power
A power of two is a number of the form 2n where n is an integer, that is, the result of exponentiation with the number two as the base and integer n as
Power_of_two
Natural number
strip of seven rectangular stamps. 115 is also a heptagonal pyramidal number. The 115th Woodall number, 115 ⋅ 2 115 − 1 = 4 776 913 109 852 041 418 248
115_(number)
Natural number
9 (nine) is the natural number following 8 and preceding 10. Circa 300 BC, as part of the Brahmi numerals, various Indians wrote a digit 9 similar in shape
9
Area of a right triangle with rational-numbered sides
In number theory, a congruent number is a positive integer that is the area of a right triangle with three rational number sides. A more general definition
Congruent_number
Number that represents a hexagon with a dot in the center
mathematics and combinatorics, a centered hexagonal number, or centered hexagon number, is a centered figurate number that represents a hexagon with a dot in the
Centered_hexagonal_number
Recursive integer sequence
they were previously discovered in the 1730s by Minggatu. The n-th Catalan number can be expressed directly in terms of the central binomial coefficients
Catalan_number
Natural number
11 (eleven) is the natural number following 10 and preceding 12. It is the smallest number whose name in English has three syllables. "Eleven" derives
11_(number)
Number that is less than the sum of its proper divisors
In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The
Abundant_number
Integer having only small prime factors
In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number is
Smooth_number
Number of form 2^(2^p-1)-1 with prime exponent
In mathematics, a double Mersenne number is a Mersenne number of the form M M p = 2 2 p − 1 − 1 {\displaystyle M_{M_{p}}=2^{2^{p}-1}-1} where p {\displaystyle
Double_Mersenne_number
Natural number, composite number
There are fourteen elements in a regular heptagon (where there are seven vertices and edges), and the total number of diagonals between all its vertices
14_(number)
Numbers with a certain property involving recursive summation
In number theory, a happy number is a number which eventually reaches 1 when the number is replaced by the sum of the square of each digit. For instance
Happy_number
Square of a triangular number
In number theory, the sum of the first n cubes is the square of the nth triangular number. That is, 1 3 + 2 3 + 3 3 + ⋯ + n 3 = ( 1 + 2 + 3 + ⋯ + n ) 2
Squared_triangular_number
Number, non-palindrome after repeated sum with reverse
numbers exist? More unsolved problems in mathematics A Lychrel number is a natural number that cannot form a palindrome through the iterative process of
Lychrel_number
Type of figurate number
In mathematics, a polygonal number is a number that counts dots arranged in the shape of a regular polygon. These are one type of 2-dimensional figurate
Polygonal_number
Infinite integer series where the next number is the sum of the two preceding it
numbers two terms apart in the Fibonacci sequence results in the Lucas number in between. The first few Lucas numbers are 2, 1, 3, 4, 7, 11, 18, 29, 47
Lucas_number
Type of figurate number
A nonagonal number, or an enneagonal number, is a figurate number that extends the concept of triangular and square numbers to the nonagon (a nine-sided
Nonagonal_number
Two or more natural numbers with a common abundancy index
In number theory, friendly numbers are two or more natural numbers with a common abundancy index, the ratio between the sum of divisors of a number and
Friendly_number
Mathematical concept in prime numbers
power. In particular, a number that has two distinct representations as a sum of two squares is composite. Every idoneal number generates a set containing
Idoneal_number
Number that remains the same when its digits are reversed
A palindromic number (also known as a numeral palindrome or a numeric palindrome) is a number (such as 16361) that remains the same when its digits are
Palindromic_number
Integer divisible by sum of its digits
In recreational mathematics, a Harshad number (or Niven number) in a given number base is an integer that is divisible by the sum of its digits when written
Harshad_number
Number used to approximate the square root of 2
starts with 0 and 1, and then each Pell number is the sum of twice the previous Pell number, plus the Pell number before that. The first few terms of the
Pell_number
Prime number of the form 2^n – 1
mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer
Mersenne_prime
Number raised to the third power
algebra, the cube of a number n is its third power, that is, the result of multiplying three instances of n together. The cube of a number n is denoted n3,
Cube_(algebra)
Type of figurate number
A hexagonal number is a figurate number. The nth hexagonal number hn is the number of distinct dots in a pattern of dots consisting of the outlines of
Hexagonal_number
Numbers that evenly divide powers of 60
and have different names coming from their different areas of study. In number theory, these numbers are called 5-smooth, because they can be characterized
Regular_number
Integer whose multiples are digit rotations
A cyclic number is an integer for which cyclic permutations of the digits are successive integer multiples of the number. The most widely known is the
Cyclic_number
Iterative algorithm on numbers
In number theory, Kaprekar's routine is an iterative algorithm named after its inventor, Indian mathematician D. R. Kaprekar. Each iteration starts with
Kaprekar's_routine
Polyhedral number representing a tetrahedron
A tetrahedral number, or triangular pyramidal number, is a figurate number that represents a pyramid with a triangular base and three sides, called a tetrahedron
Tetrahedral_number
Numbers parameterizing ways to partition a set
particularly in combinatorics, a Stirling number of the second kind (or Stirling partition number) is the number of ways to partition a set of n objects
Stirling numbers of the second kind
Stirling_numbers_of_the_second_kind
Count of the possible partitions of a set
2,5,15,52,203,877,4140,\dots } (sequence A000110 in the OEIS). The Bell number B n {\displaystyle B_{n}} counts the different ways to partition a set that
Bell_number
Numbers whose sum of divisors is twice the number plus 1
unsolved problems in mathematics In mathematics, a quasiperfect number is a natural number n for which the sum of all its divisors (the sum-of-divisors function
Quasiperfect_number
Ten raised to an integer power
the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one
Power_of_10
Integer filtered out using a sieve similar to that of Eratosthenes
In number theory, a lucky number is a natural number in a set which is generated by a certain "sieve". This sieve is similar to the sieve of Eratosthenes
Lucky_number
Class of natural numbers with many divisors
In number theory, a superior highly composite number is a natural number which, in a particular rigorous sense, has many divisors. Particularly, it is
Superior highly composite number
Superior_highly_composite_number
Number that is the result of operation on its own digits
A Friedman number is an integer, which represented in a given numeral system, is the result of a non-trivial expression using all its own digits in combination
Friedman_number
Number that cannot be written as an aliquot sum
In mathematics, an untouchable number is a positive integer that cannot be expressed as the sum of all the proper divisors of any positive integer. That
Untouchable_number
Class of binary number
In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of
Evil_number
Number of points in an octagonal arrangement
In mathematics, an octagonal number is a figurate number. The nth octagonal number on is the number of dots in a pattern of dots consisting of the outlines
Octagonal_number
Natural number with a decimal representation made of repeated instances of the same digit
or sometimes monodigit is a natural number composed of repeated instances of the same digit in a positional number system (often implicitly decimal). The
Repdigit
Base-dependent property of integers
In mathematics, a natural number in a given number base is a p {\displaystyle p} -Kaprekar number if the representation of its square in that base can
Kaprekar_number
Numbers whose prime factors all divide the number more than once
every prime number p dividing m, p2 also divides m. Equivalently, a powerful number is the product of a square and a cube, that is, a number m of the form
Powerful_number
Number sequence 3,0,2,3,2,5,5,7,10,...
} The number of different maximal independent sets in an n-vertex cycle graph is counted by the nth Perrin number for n ≥ 2. The solution
Perrin_number
Concept in combinatorics
In mathematics, the cake number, denoted by Cn, is the maximum of the number of regions into which a 3-dimensional cube can be partitioned by exactly
Cake_number
Type of composite number
In number theory, a Giuga number is a composite number n {\displaystyle n} such that for each of its distinct prime factors p i {\displaystyle p_{i}}
Giuga_number
Type of Poulet number
In number theory, a super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d {\displaystyle d} divides 2 d − 2 {\displaystyle
Super-Poulet_number
Product of two prime numbers
In number theory, a semiprime is a natural number that is the product of exactly two prime numbers. The two primes in the product may equal each other
Semiprime
Integers occurring in the coefficients of the Taylor series of 1/cosh t
combinatorics, specifically when counting the number of alternating permutations of a set with an even number of elements. The odd-indexed Euler numbers
Euler_number
Size of a geometric arrangement of points
The term figurate number is used by different writers for members of different sets of numbers, generalizing from triangular numbers to different shapes
Figurate_number
Number of stacked spheres in a pyramid
In mathematics, a pyramid number, or square pyramidal number, is a natural number that counts the stacked spheres in a pyramid with a square base. The
Square_pyramidal_number
Composite number in number theory
In number theory, a Carmichael number is a composite number n {\displaystyle n} which in modular arithmetic satisfies the congruence relation: b n
Carmichael_number
Type of composite number with an even number of digits
recreational mathematics, a vampire number (or true vampire number) is a composite natural number with an even number of digits, that can be factored into
Vampire_number
Sum of a number's digits
digit sum of a natural number in a given number base is the sum of all its digits. For example, the digit sum of the decimal number 9045 {\displaystyle 9045}
Digit_sum
Type of integer in number theory
In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer
Polite_number
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
Positive integer of the form (2^(2^n))+1
In mathematics, a Fermat number, named after Pierre de Fermat (1601–1665), the first known to have studied them, is a positive integer of the form: F n
Fermat_number
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