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76 (seventy-six) is the
natural number
In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers , while others start with 1, defining them as the positive in ...
following 75 and preceding 77.
In mathematics
76 is: * acomposite number
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 at least one divisor other than 1 and itself. Every positive integer is composite, prime numb ...
; a square-prime, of the form (''p''2, q) where q is a higher prime. It is the ninth of this general form and the seventh of the form (22.q).
* a Lucas number
The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence ar ...
.
* a telephone or involution number, the number of different ways of connecting 6 points with pairwise connections.
* a nontotient
In number theory, a nontotient is a positive integer ''n'' which is not a totient number: it is not in the range of Euler's totient function φ, that is, the equation φ(''x'') = ''n'' has no solution ''x''. In other words, ''n'' is a nontotie ...
.
* a 14-gonal number.
* a centered pentagonal number
In mathematics, a centered pentagonal number is a centered polygonal number, centered figurate number that represents a pentagon with a dot in the center and all other dots surrounding the center in successive pentagonal layers. The centered p ...
.
* an Erdős–Woods number
In number theory, a positive integer is said to be an Erdős–Woods number if it has the following property:
there exists a positive integer such that in the sequence of consecutive integers, each of the elements has a non-trivial common fac ...
since it is possible to find sequences of 76 consecutive integers such that each inner member shares a factor with either the first or the last member.
* with an aliquot sum
In number theory, the aliquot sum of a positive integer is the sum of all proper divisors of , that is, all divisors of other than itself.
That is,
s(n)=\sum_ d \, .
It can be used to characterize the prime numbers, perfect numbers, sociabl ...
of 64; within an aliquot sequence
In mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. If the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.
Def ...
of two composite numbers (76, 64, 63, 1,0) to the Prime in the 63-aliquot tree.
* an automorphic number
In mathematics, an automorphic number (sometimes referred to as a circular number) is a natural number in a given number base b whose square "ends" in the same digits as the number itself.
Definition and properties
Given a number base b, a natur ...
in base 10. It is one of two 2-digit numbers whose square, 5,776, and higher powers, end in the same two digits. The other is .
There are 76 unique compact uniform hyperbolic honeycombs in the third dimension
In geometry, a three-dimensional space (3D space, 3-space or, rarely, tri-dimensional space) is a mathematical space in which three values (''coordinates'') are required to determine the position of a point. Most commonly, it is the three-dim ...
that are generated from Wythoff constructions.
References
Integers {{Num-stub