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:

$\sqrt$ = 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:

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

Plugging in x = 10⁻⁶ yields $\frac1$, and $\sqrt$ = $\times \frac1$.

References

{{DEFAULTSORT:62 (Number)
Integers