A217678 Smallest k such that c*(c^2-1) divides k!, where c is the n-th perfect power.

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

Offset

2,1

Comments

All the terms of the sequence appear to be prime or twice a prime.

Links

Table of n, a(n) for n=2..59.

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: A348607 A200097 A314371 * A227452 A138306 A197257

Adjacent sequences: A217675 A217676 A217677 * A217679 A217680 A217681

Keyword

nonn

Author

Robin Garcia, Oct 10 2012

Status

approved