A075802 - OEIS

A075802

Characteristic function of perfect powers, A001597.

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, 0, 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

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OFFSET

1,1

COMMENTS

Not multiplicative: for example, a(8)=a(9)=1, but a(72)=0. - Franklin T. Adams-Watters, Sep 09 2005

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Perfect Powers.

Index entries for characteristic functions

FORMULA

a(n) = A057427(A052409(n) - 1);

a(A001597(n))=1 and a(A007916(n))=0.

MATHEMATICA

a[n_] := Boole[GCD @@ FactorInteger[n][[All, 2]] > 1]; a[1] = 1; Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Dec 12 2011 *)

PROG

(Haskell)

a075802 1 = 1

a075802 n = signum $ a052409 n - 1 -- Reinhard Zumkeller, May 26 2012

CROSSREFS

Cf. A112526.

Cf. A072292.

Sequence in context: A307424 A355448 A354868 * A112526 A307423 A355684

Adjacent sequences: A075799 A075800 A075801 * A075803 A075804 A075805

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Oct 13 2002

STATUS

approved

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