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 A178649 a(n) = product of nonsquarefree divisors of n. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A007955(n) / A078599(n) = A007955(n) / A007955(A007947(n)). 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. EXAMPLE For n = 16, set of such divisors is {4, 8, 16}; a(16) = 4*8*16 = 512. MATHEMATICA 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 *) PROG (Haskell) a178649 n = div (a007955 n) (a078599 n) -- Reinhard Zumkeller, Feb 06 2012 (PARI) a(n) = my(p=1); fordiv(n, d, if (!issquarefree(d), p*=d)); p; \\ Michel Marcus, Jul 06 2022 CROSSREFS Cf. A007947, A007955, A078599. Sequence in context: A112622 A183104 A183102 * A353976 A363919 A368000 Adjacent sequences: A178646 A178647 A178648 * A178650 A178651 A178652 KEYWORD nonn AUTHOR Jaroslav Krizek, Dec 25 2010 STATUS approved

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Last modified August 11 10:40 EDT 2024. Contains 375068 sequences. (Running on oeis4.)