62 (number)

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

In mathematics
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.
 * The 20th & 21st, 72nd & 73rd, 75th & 76th digits of pi.

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 $$\sqrt{62}$$ = $${7,874} \times \frac1{\sqrt{999,998}}$$.

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).