editing

approved

A. V. Zavarnitsine, <a href="http://arxiv.org/abs/0810.0568v1">Finite simple groups with narrow prime spectrum</a> arXiv:081.0568 and Sib. Elec. Math. Rep. 6 (2009) 1-12

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editing

editing

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a(17)=3 because there are precisely three non-Abelian finite simple groups G (viz. PSL(2,59), A_59, A_60) such that the maximal prime divisor of the order of G is the 17-th 17th prime (which is 59).

approved

editing

a(17)=3 because there are precisely three nonabelian non-Abelian finite simple groups G (viz. PSL(2,59), A_59, A_60) such that the maximal prime divisor of the order of G is the 17-th prime (which is 59).

nonn,new

nonn

Number of finite noncyclic simple groups whose maximal order prime divisor is the n-th prime

0, 0, 3, 15, 10, 27, 18, 15, 14, 8, 28, 13, 17, 22, 10, 10, 3, 27, 11, 6, 34, 14, 9, 9, 6, 5, 14, 3, 12, 16, 24, 7, 12, 14, 4, 11, 17, 7, 7, 11, 4, 25, 9, 15, 3, 16, 20, 5, 3, 14, 11, 5, 25, 9, 51, 11, 4, 13, 6, 5, 13, 19, 16, 3, 17, 15, 32, 18, 3, 6, 10, 9, 10, 16, 5, 7, 9, 5, 11, 14, 3

1,3

A. V. Zavarnitsine, <a href="http://arxiv.org/abs/0810.0568v1">Finite simple groups with narrow prime spectrum</a>

a(17)=3 because there are precisely three nonabelian finite simple groups G (viz. PSL(2,59), A_59, A_60) such that the maximal prime divisor of the order of G is the 17-th prime (which is 59).

Cf. A001034

nonn

Andrei V. Zavarnitsine (zav(AT)math.nsc.ru), Oct 03 2008

approved