# 65 (number)

 ← 64 65 66 →
Cardinalsixty-five
Ordinal65th
(sixty-fifth)
Factorization5 × 13
Divisors1, 5, 13, 65
Greek numeralΞΕ´
Roman numeralLXV
Binary10000012
Ternary21023
Octal1018
Duodecimal5512

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

## In mathematics

Sixty-five is the 23rd[1] semiprime and the 3rd of the form (5.q). It is an octagonal number.[2] It is also a Cullen number.[3] Given 65, the Mertens function returns 0.[4]

This number is the magic constant of 5 by 5 normal magic square:

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

This number is also the magic constant of n-Queens Problem for n = 5.[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).[6]

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 music

• "65 Love Affair", singer Paul Davis' hit song in 1982
• Sammy Hagar re-recorded his hit "I Can't Drive 55", with the 55 changed to 65, in 2001 for NBC's NASCAR broadcasts to reflect higher speed limits; the song was used from 2001 until 2004 to introduce Budweiser Pole Award winners on NBC and TNT broadcasts
• 65 is a commonly used abbreviation for the Sheffield, UK, post-rock band 65daysofstatic
• Referenced in "Heroes and Villains" by the Beach Boys: "At 60 and 5 / I'm very much alive / I've still got the jive / to survive with the Heroes and Villains"
• Odd Future group MellowHype has performed a song entitled "65"

## References

1. ^ Sloane, N. J. A. (ed.). "Sequence A001358". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
2. ^ "Sloane's A000567 : Octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
3. ^ "Sloane's A002064 : Cullen numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
4. ^ "Sloane's A028442 : Numbers n such that Mertens' function is zero". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
5. ^ Sloane, N. J. A. (ed.). "Sequence A006003". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
6. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.