# 496 (number) - in Mathematics

In Mathematics

496 is most notable for being a perfect number, and one of the earliest numbers to be recognized as such. As a perfect number, it is tied to the Mersenne prime 31, 25 - 1, with 24 ( 25 - 1 ) yielding 496. Also related to its being a perfect number, 496 is a harmonic divisor number, since the number of proper divisors of 496 divided by the sum of the reciprocals of its divisors, 1, 2, 4, 8, 16, 31, 62, 124, 248 and 496, (the harmonic mean), yields an integer, 5 in this case.

A triangular number and a hexagonal number, 496 is also a centered nonagonal number and a centered 11-gonal number. Being the 31st triangular number, 496 is the smallest counterexample to the hypothesis that one more than an even indexed triangular number is a prime number. It is the largest happy number less than 500.

There is no solution to the equation φ(x) = 496, making 496 a nontotient.

E8 has real dimension 496.

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