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

1,2

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.

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

Formula

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

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 *)

Crossrefs

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

Sequence in context: A273885 A363287 A174670 * A178772 A367141 A296870

Adjacent sequences: A212551 A212552 A212553 * A212555 A212556 A212557

Keyword

nonn

Author

Ben Branman, May 21 2012

Status

approved