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%I #21 Jul 06 2022 06:57:43
%S 1,1,1,4,1,1,1,32,9,1,1,48,1,1,1,512,1,162,1,80,1,1,1,9216,25,1,243,
%T 112,1,1,1,16384,1,1,1,279936,1,1,1,25600,1,1,1,176,405,1,1,7077888,
%U 49,1250,1,208
%N a(n) = product of nonsquarefree divisors of n.
%H Reinhard Zumkeller, <a href="/A178649/b178649.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A007955(n) / A078599(n) = A007955(n) / A007955(A007947(n)).
%F a(1) = 1, a(p) = 1, a(pq) = 1, a(pq...z) = 1, a(p^k) = p^(1/2*k*(k+1)-1), for p, q = primes, k = natural numbers, pq...z = product of k (k > 2) distinct primes p, q, ..., z.
%e For n = 16, set of such divisors is {4, 8, 16}; a(16) = 4*8*16 = 512.
%t Table[Times@@Select[Divisors[n],!SquareFreeQ[#]&],{n,60}] (* _Harvey P. Dale_, Nov 04 2020 *)
%t a[n_] := n^(DivisorSigma[0, n]/2) / (Times @@ FactorInteger[n][[;;,1]])^(2^(PrimeNu[n]-1)); Array[a, 100] (* _Amiram Eldar_, Jul 06 2022 *)
%o (Haskell)
%o a178649 n = div (a007955 n) (a078599 n)
%o -- _Reinhard Zumkeller_, Feb 06 2012
%o (PARI) a(n) = my(p=1); fordiv(n, d, if (!issquarefree(d), p*=d)); p; \\ _Michel Marcus_, Jul 06 2022
%Y Cf. A007947, A007955, A078599.
%K nonn
%O 1,4
%A _Jaroslav Krizek_, Dec 25 2010
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