28 (number)
28 (twenty-eight) is the natural number following 27 and preceding 29.
Twenty-eight is a composite number and the second perfect number as it is the sum of its proper divisors:
As a perfect number, it is related to the Mersenne prime 7, since
The next perfect number is 496, the previous being 6.
[1] Though perfect, 28 is not the aliquot sum of any other number other than itself; thus, it is not part of a multi-number aliquot sequence.
Twenty-eight is the sum of the totient function for the first nine integers.
[2] Since the greatest prime factor of
[3] Twenty-eight is a harmonic divisor number,[4] a happy number,[5] the 7th triangular number,[6] a hexagonal number,[7] a Leyland number of the second kind[8] (
), and a centered nonagonal number.
[9] It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).
[10] It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its decimal digits: 2, 8, 10, 18, 28...[11] There are 28 convex uniform honeycombs.
Twenty-eight is the only positive integer that has a unique Kayles nim-value.
Twenty-eight is the only known number that can be expressed as a sum of the first positive integers (
), and a sum of the first nonprimes (
[12] There are twenty-eight oriented diffeomorphism classes of manifolds homeomorphic to the 7-sphere.
[citation needed] There are 28 non-equivalent ways of expressing 1000 as the sum of two prime numbers.
[13] Twenty-eight is the smallest number that can be expressed as the sum of four nonzero squares in (at least) three ways:
