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 square-free integer between "x" and formula_26 for positive "x". Moreover, an elementary argument allows us to replace formula_26 by formula_28. The ABC conjecture would allow formula_29. If we represent a square-free number as the infinite product then we may take those formula_31 and use them as bits in a binary number with the encoding The square-free number 42 has factorization 2 × 3 × 7, or as an infinite product 2 · 3 · 5 · 7 · 11 · 13 ··· Thus the number 42 may be encoded as the binary sequence ...001011 or 11 decimal. (Note that the