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%I #12 Jun 14 2024 22:31:11
%S 2,4,12,24,48,144,1440,2880,120960,1451520,87091200,1902071808000,
%T 15184923989114880000,
%U 808017424794512875886459904961710757005754368000000000
%N Unique values, or record values, of A343743.
%C Every term in this sequence except the last is a number of least prime signature (A025487).
%C 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.
%C n z s d
%C -- -- --- ---
%C 1 46 134 180
%C 2 23 67 90
%C 3 20 30 50
%C 4 15 25 40
%C 5 11 22 33
%C 6 10 15 25
%C 7 9 9 18
%C 8 7 9 16
%C 9 6 5 11
%C 10 5 4 9
%C 11 4 3 7
%C 12 3 2 5
%C 13 2 1 3
%C 14 1 1 2
%C a(n) is the largest natural number b such that the order of the Monster group is divisible by b^z.
%D 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].
%D J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer, 3rd ed., 1999.
%F a(n) = Product_{k=1..20} prime(k)^floor(A051161(k)/z(n)).
%t f = FactorInteger[MonsterGroupM[] // GroupOrder]; DeleteDuplicates@ Table[Times @@ ((First[#]^Floor[Last[#]/z]) & /@ f), {z, Max[f[[;; , 2]]], 1, -1}] (* _Amiram Eldar_, Sep 30 2021 *)
%Y Cf. A051161, A343743.
%K nonn,fini,full
%O 1,1
%A _Hal M. Switkay_, Sep 29 2021