Sixty-four is the square of8, the cube of4, and thesixth power of2. It is the seventeenthinterprime, since it lies midway between the eighteenth and nineteenth prime numbers (61,67).[1]
Thealiquot sum of a power of two (2n) is always one less than the power of two itself, therefore the aliquot sum of 64 is63, within analiquot sequence of two composite members (64,63,41,1,0) that are rooted in the aliquot tree of the thirteenth prime, 41.[2]
64 is:
the smallest number with exactly sevendivisors,[3]
the first whole number (greater than one) that is both a perfect square, and a perfect cube,[4]
Since it is possible to find sequences of 65 consecutive integers (intervals of length 64) such that each inner member shares a factor with either the first or the last member, 64 is the seventhErdős–Woods number.[10]
Indecimal, no integer added to the sum of its own digits yields 64; hence, 64 is thetenthself number.[11]
