A348092 Unique values, or record values, of A343743.

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

Offset: 1

Author

Hal M. Switkay, Sep 29 2021

Keywords

• nonn
• fini
• full

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.

Crossrefs

Cf. A051161, A343743.

Programs

Mathematica

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

Formula

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