64 (number) 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. 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. 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 that is both a perfect square and a perfect cube. Since
Powerful number of "x"+"y"="z" in relatively prime non-cube 3-powerful numbers as follows: the triplet is a solution of the equation 32"X" + 49"Y" = 81"Z". We can construct another solution by setting "X"′ = "X"(49"Y" + 81"Z"), "Y"′ = −"Y"(32"X" + 81"Z"), "Z"′ = "Z"(32"X" − 49"Y") and omitting the common divisor. Powerful number A powerful number is a positive integer "m" such that for every prime number "p" dividing "m", "p" also divides "m". Equivalently, a powerful number is the product of a square and a cube, that is, a number "m" of the form "m" = "a""b", where "a" and