A308360 Product of positive divisors d of n that are divisible by every prime that divides n.

1, 2, 3, 8, 5, 6, 7, 64, 27, 10, 11, 72, 13, 14, 15, 1024, 17, 108, 19, 200, 21, 22, 23, 1728, 125, 26, 729, 392, 29, 30, 31, 32768, 33, 34, 35, 46656, 37, 38, 39, 8000, 41, 42, 43, 968, 675, 46, 47, 82944, 343, 500, 51, 1352, 53, 5832, 55, 21952, 57, 58, 59

Offset

1,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Formula

a(n) = n for squarefree numbers (A005117).

a(n) = A064549(n)^(A005361(n)/2). - Charlie Neder, Jun 03 2019

Example

The divisors of 12 that are divisible by both 2 and 3 are 6 and 12. So a(12) = 6 * 12 = 72.

Mathematica

Table[Sqrt[(n*Product[If[PrimeQ[d], d, 1], {d, Divisors[n]}])^Product[ FactorInteger[n][[k, 2]], {k, 1, Length[FactorInteger[n]]}]], {n, 1, 100}] (* Vaclav Kotesovec, Jun 15 2019 *)

Prog

(Magma) [1] cat [&*[d: d in Divisors(n) |  d gt 1  and #[c: c in Divisors(d) | IsPrime(c)] eq #[d: d in Divisors(n) | IsPrime(d)]]: n in [2..100]]

Crossrefs

See A005361 and A057723 for number and sum of such divisors.

Cf. A007955, A064549.

Sequence in context: A100782 A110340 A183091 * A324364 A265344 A089489

Adjacent sequences: A308357 A308358 A308359 * A308361 A308362 A308363

Keyword

nonn

Author

Jaroslav Krizek, May 22 2019

Status

approved