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%I #15 Oct 15 2012 00:56:44
%S 5,7,6,17,13,13,31,37,14,13,41,101,61,31,127,29,26,197,43,113,61,257,
%T 34,19,43,181,401,17,97,73,53,577,313,677,73,157,421,53,62,37,41,109,
%U 89,613,1297,37,137,38,761,1601,82,157,353,86,149,1013,683,73
%N Smallest k such that c*(c^2-1) divides k!, where c is the n-th perfect power.
%C All the terms of the sequence appear to be prime or twice a prime.
%e 5 is the smallest k such that 3, 4, 5 are divisors of k!.
%t nn = 2500; pp = Union[Flatten[Table[n^i, {i, Prime[Range[PrimePi[Log[2, nn]]]]}, {n, 2, nn^(1/i)}]]]; Table[f = n*(n^2 - 1); m = 1; While[Mod[m!, f] > 0, m++]; m, {n, pp}] (* _T. D. Noe_, Oct 15 2012 *)
%Y Cf. A001597 (perfect powers).
%K nonn
%O 2,1
%A _Robin Garcia_, Oct 10 2012