A212554 Products of supersingular primes (A002267).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 66, 68, 69, 70, 71, 72, 75, 76, 77, 78, 80, 81, 82, 84, 85, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, 100

Offset: 1

Author

Ben Branman, May 21 2012

Keywords

• nonn

Comments

The initial 1 is included because it has no non-supersingular prime factors.

Many of the early terms divide the order of the monster simple group (see A174670). The first n such that a(n) does not belong to A174670 is a(204)=289.

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 and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.
• A. P. Ogg, Modular functions, in The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979), pp. 521-532, Proc. Sympos. Pure Math., 37, Amer. Math. Soc., Providence, R.I., 1980.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000
• T. Gannon, Postcards from the edge, or Snapshots of the theory of generalised Moonshine, arXiv:math/0109067.
• Eric Weisstein's World of Mathematics, Supersingular Prime

Crossrefs

Cf. A002267, A174670, A108764 (products of exactly two supersingular primes).

Programs

Mathematica

ps = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}; fQ[n_] := Module[{p = Transpose[FactorInteger[n]][[1]]}, Complement[p, ps] == {}]; Join[{1}, Select[Range[2,1000], fQ]] (* T. D. Noe, May 21 2012 *)

Formula

log a(n) ~ k*n^(1/15). - Charles R Greathouse IV, Jul 18 2012