62 (number)

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62 (sixty-two) is the natural number following 61 and preceding 63.

← 61 62 63 →
Cardinalsixty-two
Ordinal62nd
(sixty-second)
Factorization2 × 31
Divisors1, 2, 31, 62
Greek numeralΞΒ´
Roman numeralLXII
Binary1111102
Ternary20223
Senary1426
Octal768
Duodecimal5212
Hexadecimal3E16

In mathematics

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62 as the sum of three distinct positive squares.

62 is:

  • the eighteenth discrete semiprime ( ) and tenth of the form (2.q), where q is a higher prime.
  • with an aliquot sum of 34; itself a semiprime, within an aliquot sequence of seven composite numbers (62,34,20,22,14,10,8,7,1,0) to the Prime in the 7-aliquot tree. This is the longest aliquot sequence for a semiprime up to 118 which has one more sequence member. 62 is the tenth member of the 7-aliquot tree (7, 8, 10, 14, 20, 22, 34, 38, 49, 62, 75, 118, 148, etc).
  • a nontotient.[1]
  • palindromic and a repdigit in bases 5 (2225) and 30 (2230)
  • the sum of the number of faces, edges and vertices of icosahedron or dodecahedron.
  • the number of faces of two of the Archimedean solids, the rhombicosidodecahedron and truncated icosidodecahedron.
  • the smallest number that is the sum of three distinct positive squares in two (or more) ways,   [2]
  • the only number whose cube in base 10 (238328) consists of 3 digits each occurring 2 times.[3]
  • The 20th & 21st, 72nd & 73rd, 75th & 76th digits of pi.[4]

Square root of 62

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As a consequence of the mathematical coincidence that 106 − 2 = 999,998 = 62 × 1272, the decimal representation of the square root of 62 has a curiosity in its digits:[5]

  = 7.874 007874 011811 019685 034448 812007 …

For the first 22 significant figures, each six-digit block is 7,874 or a half-integer multiple of it.

7,874 × 1.5 = 11,811

7,874 × 2.5 = 19,685

The pattern follows from the following polynomial series:

 

Plugging in x = 10−6 yields  , and   =  .

In science

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In other fields

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References

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  1. ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
  2. ^ "A024804: Numbers that are the sum of 3 distinct nonzero squares in 2 or more ways". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2021-03-25.
  3. ^ John D. Cook (5 February 2010). "Carnival of Mathematics #62".
  4. ^ "On the Number 62". www.wisdomportal.com. Retrieved 2021-01-21.
  5. ^ Robert Munafo. "Notable Properties of Specific Numbers".