64 (number) it is possible to find sequences of 64 consecutive integers 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 added up to its own digits yields 64, hence it is a self number. 64 is a superperfect number—a number such that σ(σ("n")) = 2"n". 64 is the index of Graham's number in the rapidly growing sequence 3↑↑↑↑3, 3 ↑ 3,… Sixty-four is: 64 (number) 64 (sixty-four) is the natural number following 63 and preceding 65. Sixty-four is the square of 8, the cube
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