65 (number)

65
Cardinal sixty-five
Ordinal 65th
(sixty-fifth)
Factorization  5 \cdot 13
Divisors 1, 5, 13, 65
Roman numeral LXV
Binary 10000012
Octal 1018
Duodecimal 5512
Hexadecimal 4116

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

Contents

In mathematics

Sixty-five is the 23rd[1] 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:


\begin{bmatrix}
 17 & 24 & 1 & 8 & 15 \\
 23 & 5 & 7 & 14 & 16 \\
 4 & 6 & 13 & 20 & 22 \\
 10 & 12 & 19 & 21 & 3 \\
 11 & 18 & 25 & 2 & 9
\end{bmatrix}.

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

In science

Astronomy

In music

In other fields

Sixty-five is:

In sports

Historical years

65 A.D., 65 B.C., 1965, 2065, etc.

References

  1. ^ (sequence A001358 in OEIS)