65 (sixty-five) is the natural number following 64 and preceding 66.

In mathematics

65 is the nineteenth distinct semiprime, (5.13); and the third of the form (5.q), where q is a higher prime. 65 has a prime aliquot sum of 199-number) within an aliquot sequence of one composite numbers (65,199-number),1,0) to the prime; as the first member' of the 199-number)-aliquot tree. It is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0. This number is the magic constant of a 5x5 normal magic square: This number is also the magic constant of n-Queens Problem for n = 5. 65 is the smallest integer that can be expressed as a sum of two distinct positive squares in two (or more) ways, 65 = 82 + 12 = 72 + 42. It appears in the Padovan sequence, preceded by the terms 28, 37, 49 (it is the sum of the first two of these). 65 is a Stirling number of the second kind, the number of ways of dividing a set of six objects into four non-empty subsets. 65 = 15 + 24 + 33 + 42 + 51. 65 is the length of the hypotenuse of 4 different Pythagorean triangles, the lowest number to have more than 2: 652 = 162 + 632 = 332 + 562 = 392 + 522 = 252 + 602. The first two are "primitive", and 65 is the lowest number to be the largest side of more than one such triple. 65 is the number of compositions of 11 into distinct parts.

In science

Astronomy

In music

In other fields