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 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