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%I #16 May 20 2023 04:34:09
%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 k such that Sum_{d|k, d = 1 or not a perfect power} mu(k/d) is nonzero.
%C First differs from A038109 at a(53) = 216, A038109(53) = 220.
%C Contains all prime powers (A000961).
%C The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 3, 26, 254, 2557, 25663, 256765, 2567839, 25679023, 256791104, 2567912451, ... . Apparently, the asymptotic density of this sequence exists and equals 0.256791... . - _Amiram Eldar_, May 20 2023
%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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