65 (number)

(Redirected from Number 65)

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

← 64 65 66 →
Cardinalsixty-five
Ordinal65th
(sixty-fifth)
Factorization5 × 13
Divisors1, 5, 13, 65
Greek numeralΞΕ´
Roman numeralLXV
Binary10000012
Ternary21023
Senary1456
Octal1018
Duodecimal5512
Hexadecimal4116

In mathematics

edit
 
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:

 

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

edit

Astronomy

edit

In music

edit
  • "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

edit
  • 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

edit
  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. ^ OEISA024508
  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. ^ OEISA003101
  10. ^ OEISA164282
  11. ^ OEISA024409
  12. ^ Sloane, N. J. A. (ed.). "Sequence A032020 (Number of compositions (ordered partitions) of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.