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%I #23 Oct 09 2017 12:49:43
%S 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,
%T 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,
%U 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
%N Characteristic function of perfect powers, A001597.
%C Not multiplicative: for example, a(8)=a(9)=1, but a(72)=0. - _Franklin T. Adams-Watters_, Sep 09 2005
%H Reinhard Zumkeller, <a href="/A075802/b075802.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PerfectPower.html">Perfect Powers</a>.
%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>
%F a(n) = A057427(A052409(n) - 1);
%F a(A001597(n))=1 and a(A007916(n))=0.
%t a[n_] := Boole[GCD @@ FactorInteger[n][[All, 2]] > 1]; a[1] = 1; Table[a[n], {n, 1, 105}] (* _Jean-François Alcover_, Dec 12 2011 *)
%o (Haskell)
%o a075802 1 = 1
%o a075802 n = signum $ a052409 n - 1 -- _Reinhard Zumkeller_, May 26 2012
%Y Cf. A112526.
%Y Cf. A072292.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, Oct 13 2002
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