62 (number)

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title: "62 (number)" type: doc version: 1 created: 2026-02-28 author: "Wikipedia contributors" status: active scope: public tags: ["integers"] topic_path: "general/integers" source: "https://en.wikipedia.org/wiki/62_(number)" license: "CC BY-SA 4.0" wikipedia_page_id: 0 wikipedia_revision_id: 0

::data[format=table title="Infobox number"]

FieldValue
number62
divisor1, 2, 31, 62
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| number = 62 | divisor = 1, 2, 31, 62 62 (sixty-two) is the natural number following 61 and preceding 63.

In mathematics

::figure[src="https://upload.wikimedia.org/wikipedia/commons/e/ef/Square-sum-62.png" caption="62 as the sum of three distinct positive squares."] ::

62 is:

  • the eighteenth discrete semiprime (2 \times 31) 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.
  • 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, 1^2+5^2+6^2 = 2^2+3^2+7^2
  • the only number whose cube in base 10 (238328) consists of 3 digits each occurring 2 times.{{cite web |title=Carnival of Mathematics #62 |url=http://www.johndcook.com/blog/2010/02/05/carnival-of-mathematics-62/ |author=John D. Cook |date=5 February 2010
  • The 20th and 21st, the 72nd and 73rd, and the 75th and 76th digits of .

Square root of 62

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:

\sqrt{62} = 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:

\begin{align}

(1-2x)^{-\frac{1}{2}} &= 1 + x + \frac{3}{2}x^2 + \frac{5}{2}x^3 + \frac{35}{8}x^4 + \frac{63}{8}x^5 + \cdots \end{align}

Plugging in x = 10−6 yields \frac1{\sqrt{999,998}}, and \sqrt{62} = {7,874} \times \frac1{\sqrt{999,998}}.

References

References

  1. "Sloane's A005277 : Nontotients". OEIS Foundation.
  2. "A024804: Numbers that are the sum of 3 distinct nonzero squares in 2 or more ways". OEIS Foundation.
  3. "On the Number 62".
  4. Robert Munafo. "Notable Properties of Specific Numbers: 62".

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integers