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A p p e a r a n c e
F r o m W i k i p e d i a , t h e f r e e e n c y c l o p e d i a
62 (sixty-two ) is the natural number following 61 and preceding 63 .
In mathematics
[ edit ]
62 as the sum of three distinct positive squares.
62 is:
the eighteenth discrete semiprime (
2
×
31
{\displaystyle 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 .[1]
palindromic and a repdigit in bases 5 (2225 ) and 30 (22 30 )
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
{\displaystyle 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
[ 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]
62
{\displaystyle {\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:
(
1
−
2
x
)
−
1
2
=
1
+
x
+
3
2
x
2
+
5
2
x
3
+
35
8
x
4
+
63
8
x
5
+
⋯
{\displaystyle {\begin{aligned}(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{aligned}}}
Plugging in x = 10−6 yields
1
999
,
998
{\displaystyle {\frac {1}{\sqrt {999,998}}}}
, and
62
{\displaystyle {\sqrt {62}}}
=
7
,
874
×
1
999
,
998
{\displaystyle {7,874}\times {\frac {1}{\sqrt {999,998}}}}
.
In science
[ edit ]
In other fields
[ edit ]
References
[ edit ]
^ 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" .
t
e
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
R e t r i e v e d f r o m " https://en.wikipedia.org/w/index.php?title=62_(number)&oldid=1235404547 "
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