OFFSET
1,1
COMMENTS
Every term in this sequence except the last is a number of least prime signature (A025487).
In the following table, when the order of the Monster group is written in base a(n), it has exactly z zeros, s significant digits, and d = s + z total digits.
n z s d
-- -- --- ---
1 46 134 180
2 23 67 90
3 20 30 50
4 15 25 40
5 11 22 33
6 10 15 25
7 9 9 18
8 7 9 16
9 6 5 11
10 5 4 9
11 4 3 7
12 3 2 5
13 2 1 3
14 1 1 2
a(n) is the largest natural number b such that the order of the Monster group is divisible by b^z.
REFERENCES
J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites].
J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer, 3rd ed., 1999.
FORMULA
a(n) = Product_{k=1..20} prime(k)^floor(A051161(k)/z(n)).
MATHEMATICA
f = FactorInteger[MonsterGroupM[] // GroupOrder]; DeleteDuplicates@ Table[Times @@ ((First[#]^Floor[Last[#]/z]) & /@ f), {z, Max[f[[;; , 2]]], 1, -1}] (* Amiram Eldar, Sep 30 2021 *)
CROSSREFS
KEYWORD
nonn,fini,full
AUTHOR
Hal M. Switkay, Sep 29 2021
STATUS
approved