From Wikipedia, the free encyclopedia
Natural number
81 (eighty-one ) is the
natural number following
80 and preceding
82 .
In mathematics
81 is:
the
square of
9 and the second fourth-power of a prime;
3 4 .
with an
aliquot sum of
40 ; within an
aliquot sequence of three composite numbers (81,
40 ,
50 ,
43 ,
1 ,0) to the Prime in the
43 -aliquot tree.
a
perfect totient number like all
powers of three .
[1]
a
heptagonal number .
[2]
an
icosioctagonal number.
[3]
a
centered octagonal number .
[4]
a
tribonacci number .
[5]
an
open meandric number .
[6]
the ninth member of the
Mian-Chowla sequence .
[7]
a
palindromic number in bases 8 (1218 ) and 26 (3326 ).
a
Harshad number in bases 2, 3, 4, 7, 9, 10 and 13.
one of three non-trivial numbers (the other two are
1458 and
1729 ) which, when its digits (in decimal) are added together, produces a sum which, when multiplied by its reversed self, yields the original number:
8 + 1 = 9
9 × 9 = 81 (although this case is somewhat degenerate, as the sum has only a single digit).
Look up
eighty-one in Wiktionary, the free dictionary.
The inverse of 81 is 0.012345679
recurring , missing only the digit "8" from the complete set of digits. This is an example of the general rule that, in base b ,
1
(
b
−
1
)
2
=
0.
012
⋯
(
b
−
4
)
(
b
−
3
)
(
b
−
1
)
¯
,
{\displaystyle {\frac {1}{\left(b-1\right)^{2}}}=0.{\overline {012\cdots (b-4)(b-3)(b-1)}},}
omitting only the digit b −2.
In astronomy
In other fields
Eighty-one is also:
See also
References
^
Sloane, N. J. A. (ed.).
"Sequence A082897 (Perfect totient numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000566 (Heptagonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A161935 (28-gonal numbers.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A016754 (Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A000073 (Tribonacci numbers)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005316 (Meandric numbers: number of ways a river can cross a road n times.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^
Sloane, N. J. A. (ed.).
"Sequence A005282 (Mian-Chowla sequence)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
^ Kovalevski, Serge F. (November 28, 2013),
"Despite Outlaw Image, Hells Angels Sue Often" ,
The New York Times .
^ Ansorge, Peter (9 September 2011).
"Aleister Reid obituary" . The Guardian . London. Retrieved 24 May 2012 .
^
The Eighty-One Brothers , sacred-texts.com
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