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{{Infobox number |
{{Infobox number |
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| number = |
| number = 62 |
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| divisor = |
| divisor = 1, 2, 31, 62 |
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}} |
}} |
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''' |
'''62''' ('''sixty-two''') is the [[natural number]] following [[61 (number)|61]] and preceding [[63 (number)|63]]. |
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== In mathematics == |
== In mathematics == |
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[[File:Square-sum-62.png|thumb|62 as the sum of three distinct positive squares.]] |
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'''62''' is: |
'''62''' is: |
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* the eighteenth discrete [[semiprime]] (<math>2 \times 31</math>) and tenth of the form (2.q), where q is a higher prime. |
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*The 43rd [[composite number]] with the [[divisor]]s 2 and 31, being the eighteenth discrete [[semiprime]]. |
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* with an [[aliquot sum]] of [[34 (number)|34]]; itself a [[semiprime]], within an [[aliquot sequence]] of seven composite numbers (62,[[34 (number)|34]],[[20 (number)|20]],[[22 (number)|22]],[[14 (number)|14]],[[10 (number)|10]],[[8 (number)|8]],[[7 (number)|7]],[[1 (number)|1]],0) to the Prime in the [[7 (number)|7]]-aliquot tree. This is the longest aliquot sequence for a semiprime up to [[118 (number)|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). |
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*a [[nontotient]].<ref>{{Cite web|url=https://oeis.org/A005277|title=Sloane's A005277 : Nontotients|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}</ref> |
*a [[nontotient]].<ref>{{Cite web|url=https://oeis.org/A005277|title=Sloane's A005277 : Nontotients|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2016-05-30}}</ref> |
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*palindromic and a [[repdigit]] in bases 5 (222<sub>5</sub>) and 30 (22<sub>30</sub>) |
*palindromic and a [[repdigit]] in bases 5 (222<sub>5</sub>) and 30 (22<sub>30</sub>) |
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*the sum of the number of faces, edges and vertices of [[icosahedron]] or [[dodecahedron]]. |
*the sum of the number of faces, edges and vertices of [[icosahedron]] or [[dodecahedron]]. |
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*the number of faces of two of the [[Archimedean solid]]s, the [[rhombicosidodecahedron]] and [[truncated icosidodecahedron]]. |
*the number of faces of two of the [[Archimedean solid]]s, the [[rhombicosidodecahedron]] and [[truncated icosidodecahedron]]. |
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*the smallest number that is the sum of three distinct positive squares in two ways, <math>1^2+5^2+6^2 = 2^2+3^2+7^2</math> <ref>{{Cite web|url=https://oeis.org/A024804|title=A024804: Numbers that are the sum of 3 distinct nonzero squares in 2 or more ways|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2021-03-25}}</ref> |
*the smallest number that is the sum of three distinct positive squares in two (or more) ways, <math>1^2+5^2+6^2 = 2^2+3^2+7^2</math> <ref>{{Cite web|url=https://oeis.org/A024804|title=A024804: Numbers that are the sum of 3 distinct nonzero squares in 2 or more ways|website=The On-Line Encyclopedia of Integer Sequences|publisher=OEIS Foundation|access-date=2021-03-25}}</ref> |
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*the only number whose [[cube (algebra)|cube]] in base 10 (238328) consists of 3 digits each occurring 2 times.<ref>{{cite web |
*the only number whose [[cube (algebra)|cube]] in base 10 (238328) consists of 3 digits each occurring 2 times.<ref>{{cite web |
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|title=Carnival of Mathematics #62 |
|title=Carnival of Mathematics #62 |
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|date=5 February 2010 |
|date=5 February 2010 |
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}}</ref> |
}}</ref> |
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*the tenth member of the 7-aliquot tree (7, 8, 10, 14, 20, 22, 34, 38, 49, 62, 75, 118, 148, etc). It has an [[aliquot sum]] of 34; itself a discrete [[semiprime]], and its [[aliquot sequence]] is: 62,34,20,22,14,10,8,7,1,0. |
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*The 20th & 21st, 72nd & 73rd, 75th & 76th digits of pi.<ref name=":0">{{Cite web|title=On the Number 62|url=http://www.wisdomportal.com/Numbers/62.html|access-date=2021-01-21|website=www.wisdomportal.com}}</ref> |
*The 20th & 21st, 72nd & 73rd, 75th & 76th digits of pi.<ref name=":0">{{Cite web|title=On the Number 62|url=http://www.wisdomportal.com/Numbers/62.html|access-date=2021-01-21|website=www.wisdomportal.com}}</ref> |
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===Square root of 62=== |
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As a consequence of the [[mathematical coincidence]] that 10<sup>6</sup> − 2 = 999,998 = 62 × 127<sup>2</sup>, the decimal representation of the square root of 62 has a curiosity in its digits:<ref>{{cite web|url=https://www.mrob.com/pub/math/numbers-3.html|title=Notable Properties of Specific Numbers|author=Robert Munafo}}</ref> |
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<math>\sqrt{62}</math> = 7.874 007874 011811 019685 034448 812007 … |
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For the first 22 significant figures, each six-digit block is 7,874 or a half-integer multiple of it. |
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7,874 × 1.5 = 11,811 |
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7,874 × 2.5 = 19,685 |
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The pattern follows from the following polynomial series: |
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<math display="block">\begin{align} |
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(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 |
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\end{align} |
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</math> |
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Plugging in x = 10<sup>−6</sup> yields <math>\frac1{\sqrt{999,998}}</math>, and <math>\sqrt{62}</math> = <math>{7,874} \times \frac1{\sqrt{999,998}}</math>. |
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== In science == |
== In science == |
Latest revision as of 03:44, 19 July 2024
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Cardinal | sixty-two | |||
Ordinal | 62nd (sixty-second) | |||
Factorization | 2 × 31 | |||
Divisors | 1, 2, 31, 62 | |||
Greek numeral | ΞΒ´ | |||
Roman numeral | LXII | |||
Binary | 1111102 | |||
Ternary | 20223 | |||
Senary | 1426 | |||
Octal | 768 | |||
Duodecimal | 5212 | |||
Hexadecimal | 3E16 |
62 (sixty-two) is the natural number following 61 and preceding 63.
In mathematics
[edit]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
[edit]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
[edit]- Sixty-two is the atomic number of samarium, a lanthanide.
In other fields
[edit]- 62 is the code for international direct dial calls to Indonesia.
- In the 1998 Home Run Race, Mark McGwire hit his 62nd home run on September 8, breaking the single-season record. Sammy Sosa hit his 62nd home run just days later on September 13.
- Under Social Security (United States), the earliest age at which a person may begin receiving retirement benefits (other than disability).
References
[edit]- ^ "Sloane's A005277 : Nontotients". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-30.
- ^ "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.
- ^ John D. Cook (5 February 2010). "Carnival of Mathematics #62".
- ^ "On the Number 62". www.wisdomportal.com. Retrieved 2021-01-21.
- ^ Robert Munafo. "Notable Properties of Specific Numbers".