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 if and only if all abelian groups of order "n" are isomorphic, which is the case if and only if any such group is cyclic. This follows from the classification of finitely generated abelian groups. A integer "n" is square-free if and only if the factor ring Z / "nZ (see modular arithmetic) is a product of fields. This follows from the Chinese remainder theorem and the fact that a ring of the form Z / "kZ is a field if and only if "k" is a prime. For every positive integer "n", the set of all positive divisors of