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A304365 Numbers n such that Sum_{d|n, d = 1 or not a perfect power} mu(n/d) is nonzero. 4

%I

%S 1,4,9,12,18,20,25,28,36,44,45,49,50,52,60,63,68,72,75,76,84,90,92,98,

%T 99,100,108,116,117,121,124,126,132,140,144,147,148,150,153,156,164,

%U 169,171,172,175,180,188,196,198,200,204,207,212,216,220,225,228,234

%N Numbers n such that Sum_{d|n, d = 1 or not a perfect power} mu(n/d) is nonzero.

%C First differs from A038109 at a(53) = 216, A038109(53) = 220.

%C Contains all prime powers (A000961).

%H Andrew Howroyd, <a href="/A304365/b304365.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[100],Sum[If[GCD@@FactorInteger[d][[All,2]]===1,MoebiusMu[#/d],0],{d,Divisors[#]}]=!=0&]

%o (PARI) ok(n)={sumdiv(n, d, if(ispower(d), 0, moebius(n/d))) <> 0} \\ _Andrew Howroyd_, Aug 26 2018

%Y Cf. A000005, A000961, A001221, A001597, A001694, A005117, A007916, A008683, A091050, A304326, A304327, A304362, A304364, A304369.

%K nonn

%O 1,2

%A _Gus Wiseman_, May 11 2018

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Last modified November 14 22:32 EST 2019. Contains 329134 sequences. (Running on oeis4.)