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 A108764 Products of exactly two supersingular primes (A002267). 3

%I

%S 4,6,9,10,14,15,21,22,25,26,33,34,35,38,39,46,49,51,55,57,58,62,65,69,

%T 77,82,85,87,91,93,94,95,115,118,119,121,123,133,141,142,143,145,155,

%U 161,169,177,187,203,205,209,213,217,221,235,247,253,287,289,295,299

%N Products of exactly two supersingular primes (A002267).

%C There are exactly 15 supersingular primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59 and 71 (A002267). The supersingular primes are exactly the set of primes that divide the group order of the Monster group.

%C Peter Luschny's link shows how this sequence may be connected to Schinzel-Sierpinski conjecture and the Calkin-Wilf tree.

%D E. Dijkstra, Selected Writings on Computing, Springer, 1982, p. 232.

%D Ogg, A. P. "Modular Functions." In The Santa Cruz Conference on Finite Groups. Held at the University of California, Santa Cruz, Calif., 1979 (Ed. B. Cooperstein and G. Mason). Providence, RI: Amer. Math. Soc., pp. 521-532, 1980.

%D Silverman, J. H. The Arithmetic of Elliptic Curves II. New York: Springer-Verlag, 1994.

%H T. D. Noe, <a href="/A108764/b108764.txt">Table of n, a(n) for n = 1..120</a>

%H N. Calkin and H. S. Wilf, <a href="http://www.math.upenn.edu/~wilf/website/recounting.pdf">Recounting the rationals</a>, Amer. Math. Monthly, 107 (No. 4, 2000), pp. 360-363.

%H Matthew M. Conroy, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL4/CONROY/conroy.html">A sequence related to a conjecture of Schinzel</a>, J. Integ. Seqs. Vol. 4 (2001), #01.1.7.

%H J. H. Conway and S. P. Norton, <a href="http://blms.oxfordjournals.org/content/11/3/308.extract">Monstrous Moonshine</a>, Bull. Lond. Math. Soc. 11 (1979) 308-339.

%H J. H. Conway, R. K. Guy, W. A. Schneeberger and N. J. A. Sloane, <a href="http://neilsloane.com/doc/primary.html">The Primary Pretenders</a>, Acta Arith. 78 (1997), 307-313.

%H P. D. T. A. Elliott, <a href="http://gdz.sub.uni-goettingen.de/dms/resolveppn/?PPN=GDZPPN002212722">The multiplicative group of rationals generated by the shifted primes. I.</a>, J. Reine Angew. Math. 463 (1995), 169-216.

%H P. D. T. A. Elliott, <a href="http://dx.doi.org/10.1515/crll.2000.017">The multiplicative group of rationals generated by the shifted primes. II.</a> J. Reine Angew. Math. 519 (2000), 59-71.

%H Peter Luschny, <a href="http://oeis.org/wiki/User:Peter_Luschny/SchinzelSierpinskiConjectureAndCalkinWilfTree">The Schinzel-Sierpinski conjecture and the Calkin-Wilf tree</a>.

%H A. Schinzel and W. Sierpinski, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa4/aa432.pdf">Sur certaines hypotheses concernant les nombres premiers</a>, Acta Arithmetica 4 (1958), 185-208; erratum 5 (1958) p. 259.

%H Eric Weisstein et al., <a href="http://mathworld.wolfram.com/SupersingularPrime.html">Supersingular Prime.</a>

%F {a(n)} = {p*q: p in A002267 and q in A002267}.

%e 1207 = 17 * 71, 3337 = 47 * 71.

%t Union[ Times @@@ Tuples[{2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 41, 47, 59, 71}, 2]] (*_Robert G. Wilson v_, Feb 11 2011 *)

%Y Cf. A001358, A002267.

%K easy,fini,full,nonn

%O 1,1

%A _Jonathan Vos Post_, Jun 17 2005

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