Natural number
92 (ninety-two ) is the
natural number following
91 and preceding
93 .
In mathematics
Form
92 is a
composite number of the general form p 2 q , where q is a higher
prime (
23 ). It is the tenth of this form and the eighth of the form 22 q .
Properties
92 has an
aliquot sum of
76 , within an
aliquot sequence of five numbers (92,
76 ,
64 ,
63 ,
41 ) before reaching 1.
44 , the
totient of 92, is also the
composite index of 63,
[1] where the
reduced totient of 92 is
22 .
[2] 41 is the thirteenth
prime number and sixth
super-prime . Its
arithmetic mean of its six divisors
[3] is twenty-eight,
[4]
[5] where (
6 ,
28 ) represent the first two
perfect numbers .
[6] It is the sixtieth
arithmetic number , where
60 is the second
unitary perfect number (the next such number is
90 ). For
n
=
8
{\displaystyle n=8}
, there are 92 solutions in the
n-Queens Problem . 92 is the eighth
pentagonal number .
[7] 92 is an
Erdős–Woods number , since it is possible to find sequences of 92 consecutive integers such that each inner member shares a factor with either the first or the last member.
[8]
There are 92 "atomic elements" in
John Conway's
look-and-say sequence , corresponding to the 92 non-transuranic elements in the chemist's
periodic table .
Solids
The most
faces or vertices an
Archimedean or
Catalan solid can have is 92: the
snub dodecahedron has 92 faces while its dual polyhedron, the
pentagonal hexecontahedron , has 92 vertices. On the other hand, as a
simple polyhedron , the
final stellation of the icosahedron has 92 vertices.
There are 92
Johnson solids .
Abstract algebra
92 is the total number of
objects that are
permuted by the series of five
finite, simple
Mathieu groups
M
n
{\displaystyle \mathbb {M} _{n}}
(collectively), as defined by permutations based on elements
n
∈
{
11
,
12
,
22
,
23
,
24
}
{\displaystyle n\in \{11,12,22,23,24\}}
. Half of 92 is
46 (the largest even number that is not the sum of two
abundant numbers ), which is the number of
maximal subgroups of the
friendly giant
F
1
{\displaystyle \mathbb {F} _{1}}
, the largest "
sporadic " finite simple group.
In different bases
92 is
palindromic in other bases, where it is represented as 232
6 , 1617 , 4422 , and 2245 .
There are 92 numbers
n
{\displaystyle n}
such that
2
n
{\displaystyle 2^{n}}
does not contain all digits in
base ten (the largest such number is
168 , where
68 is the smallest number with such a representation containing all digits, followed by
70 and
79 ).
[9]
In science
In other fields
Ninety-two is also:
The code for
international direct dial phone calls to
Pakistan .
The numeric code for the
Hauts-de-Seine
department of
France . The number is reflected in the department's
postal code , plus the names of at least three local sports clubs, specifically
Racing 92 in rugby union and
Metropolitans 92 and
Nanterre 92 in basketball.
In the title of the book Ninety-two in the Shade , by
Thomas McGuane .
The 92nd Tiger book by Michael Gilbert.
The House on 92nd Street , a 1945 film.
The model number of the gray
Texas Instruments
TI-92 graphing calculator.
The
Beretta 92 series of semi-automatic pistols.
The "Illustrious 92" or "Glorious 92":
Massachusetts legislators who refused to rescind the
Massachusetts Circular Letter soliciting other
British colonies' support in resistance to the
Townshend Acts prior to the
American Revolution . Analogous to the number
45 in reference to the protests of
John Wilkes against British corruption.
The
ISBN Group Identifier for books published by international publishers such as
UNESCO .
The number which runs through almost every single of British film-maker
Peter Greenaway 's films. This number has special association with the fictional character of Greenaway's creation,
Tulse Luper . It is said the number itself is based on a mathematical error in calculations concerning
John Cage 's work
Indeterminacy . See
The Falls for extensive use of this number.
"92", a song by
Avail from their 1996 album
4am Friday .
STS-92
Space Shuttle Discovery mission, on October 11, 2000, to the
International Space Station .
According to
Guinness World Records ,
Taumatawhakatangihangakoauauotamateaurehaeaturipukakapikimaungahoronukupokaiwhenuakitanatahu is the longer version of the longest place name in the world, with 92 letters.
The
92nd Street Y in
Manhattan .
Vehicles
In sports
See also
References
^
Sloane, N. J. A. (ed.).
"Sequence A002808 (The composite numbers.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
Sloane, N. J. A. (ed.).
"Sequence A002322 (Reduced totient function psi(n): least k such that x^k congruent 1 (mod n) for all x prime to n; also known as the Carmichael lambda function (exponent of unit group mod n); also called the universal exponent of n.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
Sloane, N. J. A. (ed.).
"Sequence A000005 (d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
Sloane, N. J. A. (ed.).
"Sequence A003601" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
Sloane, N. J. A. (ed.).
"Sequence A102187 (Arithmetic means of divisors of arithmetic numbers (arithmetic numbers, A003601, are those for which the average of the divisors is an integer.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
Sloane, N. J. A. (ed.).
"Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-05-15 .
^
"Sloane's A000326 : Pentagonal numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-29 .
^
"Sloane's A059756 : Erdős-Woods numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-29 .
^
Sloane, N. J. A. (ed.).
"Sequence A130696 (Numbers k such that 2^k does not contain all ten decimal digits.)" . The
On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2024-02-27 .
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000