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 triangular number Square triangular number In mathematics, a square triangular number (or triangular square number) is a number which is both a triangular number and a perfect square. There are infinitely many square triangular numbers; the first few are: Write for the th square triangular number, and write and for the sides of the corresponding square and triangle, so that Define the "triangular root" of a triangular number to be . From this definition and the quadratic formula, Therefore, is triangular ( is an integer) if and only if is square. Consequently, a square number is also triangular if and only if