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A348092 Unique values, or record values, of A343743.

%I A348092 #12 Jun 14 2024 22:31:11
%S A348092 2,4,12,24,48,144,1440,2880,120960,1451520,87091200,1902071808000,
%T A348092 15184923989114880000,
%U A348092 808017424794512875886459904961710757005754368000000000
%N A348092 Unique values, or record values, of A343743.
%C A348092 Every term in this sequence except the last is a number of least prime signature (A025487).
%C A348092 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 A348092    n  z   s   d
%C A348092   -- -- --- ---
%C A348092    1 46 134 180
%C A348092    2 23  67  90
%C A348092    3 20  30  50
%C A348092    4 15  25  40
%C A348092    5 11  22  33
%C A348092    6 10  15  25
%C A348092    7  9   9  18
%C A348092    8  7   9  16
%C A348092    9  6   5  11
%C A348092   10  5   4   9
%C A348092   11  4   3   7
%C A348092   12  3   2   5
%C A348092   13  2   1   3
%C A348092   14  1   1   2
%C A348092 a(n) is the largest natural number b such that the order of the Monster group is divisible by b^z.
%D A348092 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 A348092 J. H. Conway, N. J. A. Sloane, Sphere Packings, Lattices, and Groups. Springer, 3rd ed., 1999.
%F A348092 a(n) = Product_{k=1..20} prime(k)^floor(A051161(k)/z(n)).
%t A348092 f = FactorInteger[MonsterGroupM[] // GroupOrder]; DeleteDuplicates@ Table[Times @@ ((First[#]^Floor[Last[#]/z]) & /@ f), {z, Max[f[[;; , 2]]], 1, -1}] (* _Amiram Eldar_, Sep 30 2021 *)
%Y A348092 Cf. A051161, A343743.
%K A348092 nonn,fini,full
%O A348092 1,1
%A A348092 _Hal M. Switkay_, Sep 29 2021