Natural number
92 (ninety-two ) is the natural number following91 and preceding93 .
92 is acomposite number of the general formp 2 q , whereq is a higherprime (23 ). It is the tenth of this form and the eighth of the form 22 q .
92 has analiquot sum of76 , within analiquot sequence of five numbers (92,76 ,64 ,63 ,41 ) before reaching 1.44 , thetotient of 92, is also thecomposite index of 63,[ 1] reduced totient of 92 is22 .[ 2] prime number and sixthsuper-prime . Itsarithmetic mean of its six divisors[ 3] [ 4] [ 5] 6 ,28 ) represent the first twoperfect numbers .[ 6] arithmetic number , where60 is the secondunitary perfect number (the next such number is90 ). Forn = 8 {\displaystyle n=8} n-Queens Problem . 92 is the eighthpentagonal number .[ 7] 92 is anErdős–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" inJohn Conway's look-and-say sequence , corresponding to the 92 non-transuranic elements in the chemist'speriodic table .
The mostfaces or vertices anArchimedean orCatalan solid can have is 92: thesnub dodecahedron has 92 faces while its dual polyhedron, thepentagonal hexecontahedron , has 92 vertices. On the other hand, as asimple polyhedron , thefinal stellation of the icosahedron has 92 vertices.
There are 92Johnson solids
92 is the total number ofobjects that arepermuted by the series of fivefinite, simple Mathieu groups M n {\displaystyle \mathbb {M} _{n}} n ∈ { 11 , 12 , 22 , 23 , 24 } {\displaystyle n\in \{11,12,22,23,24\}} 46 (the largest even number that is not the sum of twoabundant numbers ), which is the number ofmaximal subgroups of thefriendly giant F 1 {\displaystyle \mathbb {F} _{1}} sporadic " finite simple group.
92 ispalindromic in other bases, where it is represented as 2326 7 , 4422 , and 2245 .
There are 92 numbersn {\displaystyle n} 2 n {\displaystyle 2^{n}} base ten (the largest such number is168 , where68 is the smallest number with such a representation containing all digits, followed by70 and79 ).[ 9]
Ninety-two is also:
The number which runs through almost every single of British film-makerPeter 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 concerningJohn Cage 's workIndeterminacy . SeeThe Falls ^ Sloane, N. J. A. (ed.)."Sequence A002808 (The composite numbers.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ 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.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ Sloane, N. J. A. (ed.)."Sequence A000005 (d(n) (also called tau(n) or sigma_0(n)), the number of divisors of n.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ Sloane, N. J. A. (ed.)."Sequence A003601" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ 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.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ Sloane, N. J. A. (ed.)."Sequence A000396 (Perfect numbers k: k is equal to the sum of the proper divisors of k.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-05-15 .^ "Sloane's A000326 : Pentagonal numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-05-29 .^ "Sloane's A059756 : Erdős-Woods numbers" .The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2016-05-29 .^ Sloane, N. J. A. (ed.)."Sequence A130696 (Numbers k such that 2^k does not contain all ten decimal digits.)" .TheOn-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved2024-02-27 .
100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 10,000,000,000 100,000,000,000
