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 A112526 Characteristic function for powerful numbers. 8
 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A signed multiplicative variant is defined by b(n) = a(n)*mu(n) with mu = A008683, such that b(p^e)=0 if e=1 and b(p^e)= -1 if e>1. This has Dirichlet series sum_{n>=1} b(n)/n = A005596 and sum_{n>=1} b(n)/n^2 = A065471. - R. J. Mathar, Apr 04 2011 a(n) * A008966(n) = A063524(n). - Reinhard Zumkeller, Sep 16 2011 LINKS Reinhard Zumkeller, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Powerful Number. FORMULA Multiplicative with a(p^e) = 1 - 0^(e-1), e>0 and p prime. Dirichlet G.F.: zeta(2*s)*zeta(3*s)/zeta(6*s), e.g. A082695 at s=1. a(n) = {m: Min{A124010(m,k): k=1..A001221(m)} > 1}. - Reinhard Zumkeller, Jun 03 2015 EXAMPLE a(72)=1 because 72=2^3*3^2 has all exponents > 1. MATHEMATICA cfpn[n_]:=If[n==1||Min[Transpose[FactorInteger[n]][[2]]]>1, 1, 0]; Array[ cfpn, 120] (* Harvey P. Dale, Jul 17 2012 *) PROG (Haskell) a112526 1 = 1 a112526 n = fromEnum \$ (> 1) \$ minimum \$ a124010_row n -- Reinhard Zumkeller, Jun 03 2015, Sep 16 2011 CROSSREFS Powerful numbers: A001694. Differs from perfect powers A075802 at Achilles numbers A052486. Cf. A124010, A001221, A027746. Cf. A008683, A008966, A005596, A065471, A082695, A063524. Sequence in context: A205633 A170956 A075802 * A120523 A030315 A119498 Adjacent sequences:  A112523 A112524 A112525 * A112527 A112528 A112529 KEYWORD mult,nonn AUTHOR Franklin T. Adams-Watters, Sep 09 2005 STATUS approved

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