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65 (number): Wikis

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From Wikipedia, the free encyclopedia

65
Cardinal sixty-five
Ordinal 65th
(sixty-fifth)
Factorization  5 \cdot 13
Divisors 1, 5, 13, 65
Roman numeral LXV
Binary 10000012
Octal 1018
Duodecimal 5512
Hexadecimal 4116

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

Contents

In mathematics

Sixty-five is the 19th semiprime and the 3rd of the form (5.q)it is an octagonal number. It is also a Cullen number. Given 65, the Mertens function returns 0.

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.

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).

There are only 65 known Euler's idoneal numbers.

65=15+24+33+42+51

In science

Astronomy

  • The Saros number of the solar eclipse series which began on -749 April 24 and ended on 513 May. The duration of Saros series 65 was 1262.1 years, and it contained 71 solar eclipses.
  • The Saros number of the lunar eclipse series which began on -736 August 11 and ended on 797 February. The duration of Saros series 65 was 1532.5 years, and it contained 86 lunar eclipses.

In other fields

Sixty-five is:

In sports

Historical years

65 A.D., 65 B.C., 1965, 2065, etc.


Simple English

Sixty-five is a number. It comes between sixty-four and sixty-six, and is an odd number. It is divisible by 5, and 13.

65 in some places

  • +65 is the International Calling Code for Singapore

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