104 (number)

← 103 104 105 →
← 100 101 102 103 104 105 106 107 108 109 → List of numbers Integers ← 0 100 200 300 400 500 600 700 800 900 →
Cardinal	one hundred four
Ordinal	104th (one hundred fourth)
Factorization	23 × 13
Divisors	1, 2, 4, 8, 13, 26, 52, 104
Greek numeral	ΡΔ´
Roman numeral	CIV, civ
Binary	11010002
Ternary	102123
Senary	2526
Octal	1508
Duodecimal	8812
Hexadecimal	6816

104 (one hundred [and] four) is the natural number following 103 and preceding 105.

In mathematics

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 ${\displaystyle \mathbb {B} }$ has a McKay–Thompson series, representative of a principal modular function is ${\displaystyle T_{2A}(\tau )}$, with constant term ${\displaystyle a(0)=104}$: ^[4]

${\displaystyle j_{2A}(\tau )=T_{2A}(\tau )+104={\frac {1}{q}}+104+4372q+96256q^{2}+\cdots }$

The Tits group ${\displaystyle \mathbb {T} }$, 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]

References

1. Sloane, N. J. A. (ed.). "SequenceA033950(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.
2. Sloane, N. J. A. (ed.). "SequenceA006036(Primitive pseudoperfect numbers.)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. Retrieved 2016-05-27.
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.). "SequenceA007267(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.
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.

• Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 133