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 some positive constant "c". Under the Riemann hypothesis, the error term can be further reduced to yield The asymptotic/natural density of square-free numbers is therefore where ζ is the Riemann zeta function and 1/ζ(2) is approximately 0.6079. Therefore over 3/5 of the integers are square-free. Likewise, if "Q"("x","n") denotes the number of "n"-free integers (e.g. 3-free integers being cube-free integers) between 1 and "x", one can show Since a multiple of 4 must have a square factor 4=2, it cannot occur that four consecutive integers are all square-free. On the other hand, there exist infinitely many integers "n" for which