65 (number)

Short description: Natural number

| <- 64  | 65 |  66 ->

|
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← 60 61 62 63 64 65 66 67 68 69 →

List of numbers — Integers

← 0 10 20 30 40 50 60 70 80 90 →

Cardinal| sixty-five
Ordinal| 65th
(sixty-fifth)
Factorization| 5 × 13
Divisors| 1, 5, 13, 65
Greek numeral| ΞΕ´
Roman numeral| LXV
Binary| 10000012
Ternary| 21023
Quaternary| 10014
Quinary| 2305
Senary| 1456
Octal| 1018
Duodecimal| 5512
Hexadecimal| 4116
Vigesimal| 3520
Base 36| 1T36

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

## Contents

* 1 In mathematics
* 2 In science
* 2.1 Astronomy
* 3 In music
* 4 In other fields
* 5 References

## In mathematics

65 as the sum of distinct positive squares.

65 is the nineteenth distinct semiprime,[1] (5.13); and the third of the form (5.q), where q is a higher prime.

65 has a prime aliquot sum of 19 within an aliquot sequence of one composite numbers (65,19,1,0) to the prime; as the first member' of the 19-aliquot tree.

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 a 5x5 normal magic square:

[17241815235714164613202210121921311182529].

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 (or more) ways, 65 = 82 \+ 12 = 72 \+ 42.[6]

It appears in the Padovan sequence, preceded by the terms 28, 37, 49 (it is the sum of the first two of these).[7]

65 is a Stirling number of the second kind, the number of ways of dividing a set of six objects into four non-empty subsets.[8]

65 = 15 \+ 24 \+ 33 \+ 42 \+ 51.[9]

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.[10] The first two are "primitive", and 65 is the lowest number to be the largest side of more than one such triple.[11]

65 is the number of compositions of 11 into distinct parts.[12]

## In science

* The atomic number of terbium, a lanthanide

### Astronomy

* Messier object M65, a galaxy of magnitude 10.5 in the constellation Leo
* The New General Catalogue object NGC 65, a spiral galaxy in the constellation Cetus

## 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"

## In other fields

* 65 miles per hour is a common speed limit on expressways in many U.S. states, primarily in the eastern and central United States. (In the western United States, a common speed limit is 70 m.p.h., and in some places it is 75 m.p.h.).
* +65 is the code for international direct dial telephone calls to Singapore.
* the traditional age for retirement in the United Kingdom, Germany, the United States, Canada, and several other countries.
* in the U.S., the age at which a person is eligible to obtain Medicare.
* CVN-65 is the designation of the U.S. Navy's first nuclear-powered aircraft carrier, the USS Enterprise (CVN-65).
* 65 is the minimum grade or average required to pass an exam, or a class, in some schools.
* The setting of the American classic TV series Naked City (1958–1963) was the 65th Precinct in New York City (sometimes referred to as simply "the 65").
* 65 is the number of the French department Hautes-Pyrénées.
* 65 is commonly used in names of many dishes of South India cuisine, for instance Chicken 65.
* The M-65 field jacket was commonly worn by American troops during the War in Vietnam.
* A 65th anniversary is sometimes referred to as a sapphire jubilee.
* The AGM-65 Maverick is a mass-produced air-to-ground tactical missile (AGM) designed for close air support against a wide range of targets.

## References

1. ↑ Sloane, N. J. A., ed. "Sequence A001358". OEIS Foundation. https://oeis.org/A001358.
2. ↑ "Sloane's A000567 : Octagonal numbers". OEIS Foundation. https://oeis.org/A000567.
3. ↑ "Sloane's A002064 : Cullen numbers". OEIS Foundation. https://oeis.org/A002064.
4. ↑ "Sloane's A028442 : Numbers n such that Mertens' function is zero". OEIS Foundation. https://oeis.org/A028442.
5. ↑ Sloane, N. J. A., ed. "Sequence A006003". OEIS Foundation. https://oeis.org/A006003.
6. ↑ OEIS: A024508
7. ↑ "Sloane's A000931 : Padovan sequence". OEIS Foundation. https://oeis.org/A000931.
8. ↑ "Sloane's A008277 : Triangle of Stirling numbers of the second kind". OEIS Foundation. https://oeis.org/A008277.
9. ↑ OEIS: A003101
10. ↑ OEIS: A164282
11. ↑ OEIS: A024409
12. ↑ Sloane, N. J. A., ed. "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". OEIS Foundation. https://oeis.org/A032020. Retrieved 2022-05-24.

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