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A348092
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Unique values, or record values, of A343743.
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0
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2, 4, 12, 24, 48, 144, 1440, 2880, 120960, 1451520, 87091200, 1902071808000, 15184923989114880000, 808017424794512875886459904961710757005754368000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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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.
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REFERENCES
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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.
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LINKS
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FORMULA
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a(n) = Product_{k=1..20} prime(k)^floor(A051161(k)/z(n)).
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MATHEMATICA
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f = FactorInteger[MonsterGroupM[] // GroupOrder]; DeleteDuplicates@ Table[Times @@ ((First[#]^Floor[Last[#]/z]) & /@ f), {z, Max[f[[;; , 2]]], 1, -1}] (* Amiram Eldar, Sep 30 2021 *)
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CROSSREFS
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KEYWORD
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nonn,fini,full
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AUTHOR
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STATUS
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approved
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