104 (number) explained

Number:	104
Divisor:	1, 2, 4, 8, 13, 26, 52, 104

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)).

The smallest known 4-regular matchstick graph has 104 edges and 52 vertices, where four unit line segments intersect at every vertex.^[7]

A row of four adjacent congruent rectangles can be divided into a maximum of 104 regions, when extending diagonals of all possible rectangles.^[8]

B , its McKay–Thompson series representative of a principal modular function is T _{2A} (\tau) , with constant term a( 0 ) = 104 :^[9] j _{2A} (\tau) = T _{2A} (\tau) +104 = (1)/(q) + 104 + 4372 q + 96256 q ^{2} + … 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.^[10] This is twice the dimensional representation of exceptional Lie algebra ak{f} _{4} in 52 dimensions, whose associated lattice structure 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).

See also

• List of highways numbered 104
• The years 104 BC and AD 104.

References

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

Notes and References

1. 2023-07-31 .
2. 2023-07-31 .
3. 2016-05-27 .
4. 2023-07-31 .
5. 2023-07-31 .
6. 2023-07-31 .
7. Winkler . Mike . Dinkelacker . Peter . Vogel . Stefan . New minimal (4; n)-regular matchstick graphs . Geombinatorics Quarterly . XXVII . 1 . 26–44 . . Colorado Springs, CO . 2017 . 1604.07134 . 119161796 . 1373.05125 .
8. 2022-05-09 .
9. 2023-07-31 .
10. Lubeck . Frank . Smallest degrees of representations of exceptional groups of Lie type . . 29 . 5 . 2151 . . Philadelphia, PA . 2001 . 10.1081/AGB-100002175 . 1837968 . 122060727 . 1004.20003 .