65 (number)

← 64 65 66 →
← 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
Senary	1456
Octal	1018
Duodecimal	5512
Hexadecimal	4116

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

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:

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

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 (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

See also: List of highways numbered 65

• 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.). "SequenceA001358". 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.). "SequenceA006003". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. OEIS:  A024508
7. "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
8. "Sloane's A008277 : Triangle of Stirling numbers of the second kind". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-12-24.
9. OEIS:  A003101
10. OEIS:  A164282
11. OEIS:  A024409
12. Sloane, N. J. A. (ed.). "SequenceA032020(Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2022-05-24.