A309510 - OEIS

%I #15 Jul 12 2021 15:18:44

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

%N Divisors of 196883.

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

%C This degree, as a number, has 8 divisors.

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

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

%C 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.

%H J. H. Conway and S. P. Norton, <a href="https://doi.org/10.1112/blms/11.3.308">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H Robert L. Griess, <a href="https://deepblue.lib.umich.edu/bitstream/handle/2027.42/46608/222_2005_Article_BF01389186.pdf">The Friendly Giant</a>, Invent. math. 69, 1-102 (1982).

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Griess_algebra">Griess algebra</a>

%H <a href="/index/Gre#groups">Index entries for sequences related to groups</a>

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

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

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

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

%t Divisors[196883]

%o (PARI) divisors(196883) \\ _Charles R Greathouse IV_, Jul 12 2021

%Y Cf. A199014 (divisors of 196884).

%K nonn,easy,fini,full

%O 1,2

%A _Jelle Herold_, Aug 05 2019