92 (number)

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92 (ninety-two) is the natural number following 91 and preceding 93

← 91 92 93 →
Cardinalninety-two
Ordinal92nd
(ninety-second)
Factorization22 × 23
Divisors1, 2, 4, 23, 46, 92
Greek numeralϞΒ´
Roman numeralXCII
Binary10111002
Ternary101023
Senary2326
Octal1348
Duodecimal7812
Hexadecimal5C16

In mathematics

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Form

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92 is a composite number of the general form p2q, where q is a higher prime (23). It is the tenth of this form and the eighth of the form 22q.

Properties

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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

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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

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92 is the total number of objects that are permuted by the series of five finite, simple Mathieu groups   (collectively), as defined by permutations based on elements  . 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  , the largest "sporadic" finite simple group.

In different bases

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92 is palindromic in other bases, where it is represented as 2326, 1617, 4422, and 2245.

There are 92 numbers   such that   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

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In other fields

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Ninety-two is also:

Vehicles

In sports

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See also

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References

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  1. ^ Sloane, N. J. A. (ed.). "Sequence A002808 (The composite numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
  2. ^ 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.
  3. ^ 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.
  4. ^ Sloane, N. J. A. (ed.). "Sequence A003601". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-05-15.
  5. ^ 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.
  6. ^ 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.
  7. ^ "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  8. ^ "Sloane's A059756 : Erdős-Woods numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-29.
  9. ^ 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.