104 (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. 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. 104 is also the twenty-fifth primitive semiperfect number.

The sum of all its divisors is σ(104) = 210, which is the sum of the first twenty nonzero integers, as well as the product of the first four prime numbers (2 × 3 × 5 × 7).

Its Euler totient, or the number of integers relatively prime with 104, is 48. This value is also equal to the totient of its sum of divisors, φ(104) = φ(σ(104)).

The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at every vertex.

A row of four adjacent congruent rectangles can be divided into a maximum of 104 regions, when extending diagonals of all possible rectangles.

Regarding the second largest sporadic group $$\mathbb {B}$$, its McKay–Thompson series representative of a principal modular function is $$T_{2A}(\tau)$$, with constant term $$a(0) = 104$$:


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

The Tits group $$\mathbb {T}$$, 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. This is twice the dimensional representation of exceptional Lie algebra $$\mathfrak{f}_4$$ in 52 dimensions, whose associated lattice structure $$\mathrm {F_{4}}$$ 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).