64 (number)
64 (sixty-four) is the natural number following 63 and preceding 65. In mathematics Sixty-four is the square of 8, the cube of 4, and the sixth-power of 2. It is the smallest number with exactly seven divisors. 64 is the first non-unitary sixth-power prime of the form p6 where p is a prime number. The aliquot sum of a 2-power (2n) is always one less than the 2-power itself therefore the aliquot sum of 64 is 63, within an aliquot sequence of two composite members ( 64,63,41,1,0) to the prime 41 in the 41-aliquot tree. It is the lowest positive power of two that is adjacent to neither a Mersenne prime nor a Fermat prime. 64 is the sum of Euler's totient function for the first fourteen integers. It is also a dodecagonal number and a centered triangular number. 64 is also the first whole number (greater than 1) that is both a perfect square and a perfect cube. Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is an Erdős–Woods number. In base 10, no integer