62 (number) explained

Number:	62
Divisor:	1, 2, 31, 62

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

In mathematics

62 is:

• the eighteenth discrete semiprime (

2 x 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.^[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,

1 ^{2+5} ^{2+6} ^{2} = 2 ^{2+3} ^{2+7} ^{2} ^[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

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]

\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:

$$\backslash begin$$

(1-2x)^ &= 1 + x + \fracx^2 + \fracx^3 + \fracx^4 + \fracx^5 + \cdots \end

Plugging in x = 10⁻⁶ yields

(1 {\sqrt{ 999 , 998 }})/() , and \sqrt{ 62 } = { 7 , 874 } x (1 {\sqrt{ 999 , 998 }})/() .

In science

• Sixty-two is the atomic number of samarium, a lanthanide.

In other fields

• 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).

Notes and References

1. Web site: Sloane's A005277 : Nontotients. The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. 2016-05-30.
2. Web site: 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. 2021-03-25.
3. Web site: Carnival of Mathematics #62 . John D. Cook . 5 February 2010.
4. Web site: On the Number 62. 2021-01-21. www.wisdomportal.com.
5. Web site: Notable Properties of Specific Numbers. Robert Munafo.