A343743 -id:A343743 - cp's OEIS frontend

A348092 Unique values, or record values, of A343743.

2, 4, 12, 24, 48, 144, 1440, 2880, 120960, 1451520, 87091200, 1902071808000, 15184923989114880000, 808017424794512875886459904961710757005754368000000000

Offset: 1

Hal M. Switkay, Sep 29 2021

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
  -- -- --- ---
46 134 180
23  67  90
20  30  50
15  25  40
11  22  33
10  15  25
9   9  18
7   9  16
6   5  11
5   4   9
4   3   7
3   2   5
2   1   3
1   1   2
a(n) is the largest natural number b such that the order of the Monster group is divisible by b^z.

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.

Cf. A051161, A343743.

f = FactorInteger[MonsterGroupM[] // GroupOrder]; DeleteDuplicates@ Table[Times @@ ((First[#]^Floor[Last[#]/z]) & /@ f), {z, Max[f[[;; , 2]]], 1, -1}] (* Amiram Eldar, Sep 30 2021 *)

a(n) = Product_{k=1..20} prime(k)^floor(A051161(k)/z(n)).

cp's OEIS Frontend

A348092 Unique values, or record values, of A343743.

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