A309510 Divisors of 196883.

1, 47, 59, 71, 2773, 3337, 4189, 196883

Offset: 1

Author

Jelle Herold, Aug 05 2019

Keywords

• nonn
• easy
• fini
• full

Comments

196883 = 47*59*71 is the degree of the smallest faithful complex representation of the Monster group M.

This degree, as a number, has 8 divisors.

Note that 2337 = 47*59, 3337 = 47*71 and 4189 = 59*71.

It is related to the sequence A199014 (the divisors of 196884) through a phenomenon called "monstrous moonshine", or 196884 = 196883 + 1.

More specifically (adapted from Wikipedia), the Griess algebra is a commutative non-associative algebra on a real vector space of dimension 196884 with M as its automorphism group. It is named after mathematician R. L. Griess, who constructed it in 1980 and used it in 1982 to construct M. The Monster fixes (vectorwise) a 1-space in this algebra and acts absolutely irreducibly on the 196883-dimensional orthogonal complement of this 1-space.

Links

• J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
• Robert L. Griess, The Friendly Giant, Invent. math. 69, 1-102 (1982).
• Wikipedia, Griess algebra
• Index entries for sequences related to groups

Crossrefs

Cf. A199014 (divisors of 196884).

Programs

Mathematica

Divisors[196883]

PARI

divisors(196883) \\ Charles R Greathouse IV, Jul 12 2021

Formula

a(2)*a(3) = a(5),

a(2)*a(4) = a(6),

a(3)*a(4) = a(7),

a(2)*a(3)*a(4) = a(8).