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A050328
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Number of ordered factorizations of n into squarefree numbers > 1.
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5
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1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 5, 1, 3, 3, 1, 1, 5, 1, 5, 3, 3, 1, 7, 1, 3, 1, 5, 1, 13, 1, 1, 3, 3, 3, 13, 1, 3, 3, 7, 1, 13, 1, 5, 5, 3, 1, 9, 1, 5, 3, 5, 1, 7, 3, 7, 3, 3, 1, 31, 1, 3, 5, 1, 3, 13, 1, 5, 3, 13, 1, 25, 1, 3, 5, 5, 3, 13, 1, 9, 1, 3, 1, 31, 3, 3, 3, 7, 1, 31, 3, 5, 3, 3, 3, 11, 1, 5
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OFFSET
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1,6
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COMMENTS
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a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
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LINKS
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Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
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Dirichlet g.f.: 1/(1-B(s)) where B(s) is D.g.f. of characteristic function of squarefree numbers > 1.
a(A000961(n)) = 1.
a(A002110(n)) = A000670(n).
a(n) = Sum_{d divides n, d<n} A008966(n/d)*a(d). - Vladeta Jovovic, Sep 25 2002, corrected by Antti Karttunen, May 27 2017
G.f. A(x) satisfies: A(x) = x + Sum_{k>=2} mu(k)^2*A(x^k). - Ilya Gutkovskiy, May 10 2019
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MATHEMATICA
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a[n_]:=If[n==1, n, Sum[If[(d<n && SquareFreeQ[n/d]), a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 100}] (* Indranil Ghosh, May 27 2017 *)
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PROG
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(Haskell)
import Data.List (genericIndex)
a050328 n = genericIndex a050328_list (n-1)
a050328_list = f 1 where
f x = (if x == 1 then 1 else
sum $ map (a050328 . (div x)) $ tail $ a206778_row x) : f (x + 1)
-- Reinhard Zumkeller, May 03 2013
(PARI) A050328(n) = if(1==n, n, sumdiv(n, d, if((d<n && issquarefree(n/d)), A050328(d), 0))); \\ Antti Karttunen, May 27 2017
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CROSSREFS
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Cf. A000670, A000961, A002033, A002110, A005117, A008966, A050329, A114006, A206778.
Sequence in context: A334019 A291448 A114006 * A191278 A359577 A030401
Adjacent sequences: A050325 A050326 A050327 * A050329 A050330 A050331
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower, Oct 15 1999
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STATUS
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approved
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