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

Author

Jaroslav Krizek, May 22 2019

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Cf. A007955, A064549.

Programs

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]]

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 *)

Formula

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

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