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
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.

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]

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.^[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.

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

• 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
• 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"

In other fields

Sixty-five is:

• A common speed limit, in miles per hour, 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.)
• The designation of Interstate 65, the Interstate Highway that runs from northwestern Indiana to southmost Alabama
• +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.
• The hull number 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 (1958–63) was the 65th Precinct in New York City.
• 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
• The age, in the U.S., at which a person is eligible to obtain Medicare

In sports

• MotoGP rider Loris Capirossi races with #65

References

1. (sequence A001358 in the OEIS)
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's 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.