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And we really like the number 28…
The number 28 is kinda magical. It is, in fact, a perfect number.
- It is a composite number, its proper divisors being 1, 2, 4, 7, and 14.
- As a perfect number, it is related to the Mersenne prime 7, since 22(23 – 1) = 28. The next perfect number is 496, the previous being 6.
- Twenty-eight is the third Granville number. The next Granville number is 96, the previous being 24.
- Twenty-eight is the sum of the totient function for the first nine integers.
- Twenty-eight is not the aliquot sum of any number other than itself and is therefore not a component in an aliquot sequence.
- Since the greatest prime factor of 282 + 1 = 785 is 157, which is more than 28 twice, 28 is a Størmer number.
- Twenty-eight is a harmonic divisor number, a happy number, a triangular number, a hexagonal number, and a centered nonagonal number.
- It appears in the Padovan sequence, preceded by the terms 12, 16, 21 (it is the sum of the first two of these).
- It is also a Keith number, because it recurs in a Fibonacci-like sequence started from its base 10 digits: 2, 8, 10, 18, 28…
- Twenty-eight is the third positive integer with a prime factorization of the form
where q is an odd prime.
- Twenty-eight is the ninth and last number in early Indian magic square of order 3.
- There are twenty-eight convex uniform honeycombs.
- Twenty-eight is the only positive integer that has a unique Kayles nim-value.
