65 (number)


65 is the natural number following 64 and preceding 66.

In mathematics

Sixty-five is the 23rd semiprime and the 3rd of the form. 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 5 by 5 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 ways, 65 = 82 + 12 = 72 + 42.
It appears in the Padovan sequence, preceded by the terms 28, 37, 49.
There are only 65 known Euler's idoneal numbers.
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.

In science