# 65 (number)

"LXV" redirects here. For the IATA/FAA code, see Lake County Airport (Colorado).
 ← 64 65 66 →
Cardinal sixty-five
Ordinal 65th
(sixty-fifth)
Factorization 5 × 13
Divisors 1, 5, 13, 65
Roman numeral LXV
Binary 10000012
Ternary 21023
Quaternary 10014
Quinary 2305
Senary 1456
Octal 1018
Duodecimal 5512
Vigesimal 3520
Base 36 1T36

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. 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.[2]

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.

In base 14, 65 is a cyclic number.

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

### Astronomy

• The Saros number of the series of solar eclipses that began on April 24, 749 BCE, and ended in May 513 CE. The duration of the Saros series 65 was 1262.1 years, and it contained 71 solar eclipses.
• The Saros number of the series of lunar eclipses that began on August 11, 736 BCE, and ended in February 797 CE. The duration of Saros series 65 was 1532.5 years, and it contained 86 lunar eclipses.

## 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"

Sixty-five is:

## References

1. ^ (sequence A001358 in OEIS)
2. ^ "Sloane's A006003 ", The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.