65 (number)

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← 64 65 66 →
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.

In mathematics[edit]

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]

This number is the magic constant of 5 by 5 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 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.

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[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]

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. ^ "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.