In Mathematics
Sixty-five is the 23rd semiprime and the 3rd of the form (5.q)it is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0.
Sixty-five has an aliquot sum of 19 and is the first composite number in the 19-aliquot tree.
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 (it is the sum of the first two of these).
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.
Read more about this topic: 65 (number)
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