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104 (number) - Wikipedia
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Natural number
104 (one hundred [and] four) is the natural number following 103 and preceding 105.
104 is a refactorable number[1] and a primitive semiperfect number.[2]
The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at every vertex.[3]
The second largest sporadic group B {\displaystyle \mathbb {B} } has a McKay–Thompson series, representative of a principal modular function is T 2 A ( τ ) {\displaystyle T_{2A}(\tau )} , with constant term a ( 0 ) = 104 {\displaystyle a(0)=104} :[4]
-
j 2 A ( τ ) = T 2 A ( τ ) + 104 = 1 q + 104 + 4372 q + 96256 q 2 + ⋯ {\displaystyle j_{2A}(\tau )=T_{2A}(\tau )+104={\frac {1}{q}}+104+4372q+96256q^{2}+\cdots }
The Tits group T {\displaystyle \mathbb {T} } , which is the only finite simple group to classify as either a non-strict group of Lie type or sporadic group, holds a minimal faithful complex representation in 104 dimensions.[5]
- ^ Sloane, N. J. A. (ed.). "Sequence A033950 (Refactorable numbers: number of divisors of k divides k. Also known as tau numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-07-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A006036 (Primitive pseudoperfect numbers.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-27.
- ^ 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.
- ^ 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.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2023-07-31.
- ^ 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.
Integers −1 0s
100s
200s
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400s
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600s
700s
800s
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1000s
- 100,000
- 1,000,000
- 10,000,000
- 100,000,000
- 1,000,000,000
- 10,000,000,000
- 100,000,000,000
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