In Mathematics
Forty is an octagonal number, and as the sum of the first four pentagonal numbers, it is a pentagonal pyramidal number. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10 and 20) gives 40, hence 40 is a semiperfect number.
Given 40, the Mertens function returns 0. 40 is the smallest number n with exactly 9 solutions to the equation φ(x) = n.
Forty is the number of n-queens problem solutions for n = 7.
Since 402 + 1 = 1601 is prime, 40 is a Størmer number.
40 is a repdigit in base 3 (1111) and a Harshad number in base 10.
Read more about this topic: 40 (number)
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