Английская Википедия:104 (number)
Шаблон:Infobox number 104 (one hundred [and] four) is the natural number following 103 and preceding 105.
In mathematics
104 forms the fifth Ruth-Aaron pair with 105, since the distinct prime factors of 104 (2 and 13) and 105 (3, 5, and 7) both add up to 15.[1] Also, the sum of the divisors of 104 aside from unitary divisors, is 105. With eight total divisors where 8 is the fourth largest, 104 is the seventeenth refactorable number.[2] 104 is also the twenty-fifth primitive semiperfect number.[3]
The sum of all its divisors is σ(104) = 210, which is the sum of the first twenty nonzero integers,[4] as well as the product of the first four prime numbers (2 × 3 × 5 × 7).[5]
Its Euler totient, or the number of integers relatively prime with 104, is 48.[6] This value is also equal to the totient of its sum of divisors, φ(104) = φ(σ(104)).[7]
The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at every vertex.[8]
A row of four adjacent congruent rectangles can be divided into a maximum of 104 regions, when extending diagonals of all possible rectangles.[9]
Regarding the second largest sporadic group <math>\mathbb {B}</math>, its McKay–Thompson series representative of a principal modular function is <math>T_{2A}(\tau)</math>, with constant term <math>a(0) = 104</math>:[10]
- <math>j_{2A}(\tau) = T_{2A}(\tau)+104 = \frac{1}{q} + 104 + 4372q + 96256q^2 + \cdots</math>
The Tits group <math>\mathbb {T}</math>, 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.[11] This is twice the dimensional representation of exceptional Lie algebra <math>\mathfrak{f}_4</math> in 52 dimensions, whose associated lattice structure <math>\mathrm {F_{4}}</math> forms the ring of Hurwitz quaternions that is represented by the vertices of the 24-cell — with this regular 4-polytope one of 104 total four-dimensional uniform polychora, without taking into account the infinite families of uniform antiprismatic prisms and duoprisms.
In other fields
104 is also:
- The atomic number of rutherfordium.
- The number of Corinthian columns in the Temple of Olympian Zeus, the largest temple ever built in Greece.
- The number of Symphonies written by Joseph Haydn upon which numbers are agreed (though in fact, he wrote two more: see list of symphonies by Joseph Haydn).
See also
- List of highways numbered 104
- The years 104 BC and AD 104.
References
Шаблон:Notelist Шаблон:Reflist
- Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 133
