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 A217678 Smallest k such that c*(c^2-1) divides k!, where c is the n-th perfect power. 0
 5, 7, 6, 17, 13, 13, 31, 37, 14, 13, 41, 101, 61, 31, 127, 29, 26, 197, 43, 113, 61, 257, 34, 19, 43, 181, 401, 17, 97, 73, 53, 577, 313, 677, 73, 157, 421, 53, 62, 37, 41, 109, 89, 613, 1297, 37, 137, 38, 761, 1601, 82, 157, 353, 86, 149, 1013, 683, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS All the terms of the sequence appear to be prime or twice a prime. LINKS EXAMPLE 5 is the smallest k such that 3, 4, 5 are divisors of k!. MATHEMATICA 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 *) CROSSREFS Cf. A001597 (perfect powers). Sequence in context: A220607 A200097 A314371 * A227452 A138306 A197257 Adjacent sequences:  A217675 A217676 A217677 * A217679 A217680 A217681 KEYWORD nonn AUTHOR Robin Garcia, Oct 10 2012 STATUS approved

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Last modified July 24 06:56 EDT 2021. Contains 346273 sequences. (Running on oeis4.)