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104 (number)

From Wikipedia, the free encyclopedia
Natural number
← 103104 105 →
Cardinalone hundred four
Ordinal104th
(one hundred fourth)
Factorization23 × 13
Divisors1, 2, 4, 8, 13, 26, 52, 104
Greek numeralΡΔ´
Roman numeralCIV,civ
Binary11010002
Ternary102123
Senary2526
Octal1508
Duodecimal8812
Hexadecimal6816

104 (one hundred [and] four) is thenatural number following103 and preceding105.

In mathematics

[edit]

104 is arefactorable number[1] and aprimitive semiperfect number.[2]

The smallest known 4-regularmatchstick graph has 104edges and 52vertices, where four unitline segments intersect at every vertex.[3]

Thesecond largest sporadic groupB{\displaystyle \mathbb {B} } has aMcKay–Thompson series, representative of aprincipal modular function isT2A(τ){\displaystyle T_{2A}(\tau )}, with constant terma(0)=104{\displaystyle a(0)=104}:[4]

j2A(τ)=T2A(τ)+104=1q+104+4372q+96256q2+⋯{\displaystyle j_{2A}(\tau )=T_{2A}(\tau )+104={\frac {1}{q}}+104+4372q+96256q^{2}+\cdots }

TheTits groupT{\displaystyle \mathbb {T} }, which is the onlyfinite simple group to classify as either anon-strict group ofLie type orsporadic group, holds aminimal faithful complex representation in 104 dimensions.[5]

References

[edit]
  1. ^Sloane, N. J. A. (ed.)."Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-07-31.
  2. ^Sloane, N. J. A. (ed.)."Sequence A006036 (Primitive pseudoperfect numbers.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2016-05-27.
  3. ^Winkler, Mike; Dinkelacker, Peter; Vogel, Stefan (2017). "New minimal (4; n)-regular matchstick graphs".Geombinatorics Quarterly.XXVII (1). Colorado Springs, CO:University of Colorado, Colorado Springs:26–44.arXiv:1604.07134.S2CID 119161796.Zbl 1373.05125.
  4. ^Sloane, N. J. A. (ed.)."Sequence A007267 (Expansion of 16 * (1 + k^2)^4 /(k * k'^2)^2 in powers of q where k is the Jacobian elliptic modulus, k' the complementary modulus and q is the nome.)".TheOn-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved2023-07-31.
  5. ^Lubeck, Frank (2001)."Smallest degrees of representations of exceptional groups of Lie type".Communications in Algebra.29 (5). Philadelphia, PA:Taylor & Francis: 2151.doi:10.1081/AGB-100002175.MR 1837968.S2CID 122060727.Zbl 1004.20003.
0 to 199
200 to 399
400 to 999
1000s and 10,000s
1000s
10,000s
100,000s to 10,000,000,000,000s


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