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
Square-free integer "n" becomes a partially ordered set if we use divisibility as the order relation. This partially ordered set is always a distributive lattice. It is a Boolean algebra if and only if "n" is square-free. A positive integer "n" is square-free if and only if μ("n") ≠ 0, where μ denotes the Möbius function. The Dirichlet generating function for the square-free numbers is This is easily seen from the Euler product Let "Q"("x") denote the number of square-free integers between 1 and "x" ( shifting index by 1). For large "n", 3/4 of the positive integers less than "n" are