A212554 - OEIS

%I #26 Jun 14 2024 22:31:10

%S 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,

%T 27,28,29,30,31,32,33,34,35,36,38,39,40,41,42,44,45,46,47,48,49,50,51,

%U 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

%N Products of supersingular primes (A002267).

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

%C 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.

%D 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].

%D J. H. Conway and S. P. Norton, Monstrous Moonshine, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%D 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.

%H T. D. Noe, <a href="/A212554/b212554.txt">Table of n, a(n) for n = 1..10000</a>

%H T. Gannon, <a href="http://arxiv.org/abs/math/0109067">Postcards from the edge, or Snapshots of the theory of generalised Moonshine</a>, arXiv:math/0109067.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SupersingularPrime.html">Supersingular Prime</a>

%F log a(n) ~ k*n^(1/15). - _Charles R Greathouse IV_, Jul 18 2012

%t 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 *)

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

%K nonn

%O 1,2

%A _Ben Branman_, May 21 2012