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%I #13 Sep 08 2022 08:46:21
%S 1,2,3,8,5,6,7,64,27,10,11,72,13,14,15,1024,17,108,19,200,21,22,23,
%T 1728,125,26,729,392,29,30,31,32768,33,34,35,46656,37,38,39,8000,41,
%U 42,43,968,675,46,47,82944,343,500,51,1352,53,5832,55,21952,57,58,59
%N Product of positive divisors d of n that are divisible by every prime that divides n.
%H Vaclav Kotesovec, <a href="/A308360/b308360.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = n for squarefree numbers (A005117).
%F a(n) = A064549(n)^(A005361(n)/2). - _Charlie Neder_, Jun 03 2019
%e The divisors of 12 that are divisible by both 2 and 3 are 6 and 12. So a(12) = 6 * 12 = 72.
%t 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 *)
%o (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]]
%Y See A005361 and A057723 for number and sum of such divisors.
%Y Cf. A007955, A064549.
%K nonn
%O 1,2
%A _Jaroslav Krizek_, May 22 2019
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