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A178649
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a(n) = product of nonsquarefree divisors of n.
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2
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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, 112, 1, 1, 1, 16384, 1, 1, 1, 279936, 1, 1, 1, 25600, 1, 1, 1, 176, 405, 1, 1, 7077888, 49, 1250, 1, 208
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OFFSET
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1,4
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LINKS
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FORMULA
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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.
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EXAMPLE
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For n = 16, set of such divisors is {4, 8, 16}; a(16) = 4*8*16 = 512.
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MATHEMATICA
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Table[Times@@Select[Divisors[n], !SquareFreeQ[#]&], {n, 60}] (* Harvey P. Dale, Nov 04 2020 *)
a[n_] := n^(DivisorSigma[0, n]/2) / (Times @@ FactorInteger[n][[;; , 1]])^(2^(PrimeNu[n]-1)); Array[a, 100] (* Amiram Eldar, Jul 06 2022 *)
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PROG
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(Haskell)
a178649 n = div (a007955 n) (a078599 n)
(PARI) a(n) = my(p=1); fordiv(n, d, if (!issquarefree(d), p*=d)); p; \\ Michel Marcus, Jul 06 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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