A304369 - OEIS

%I #15 May 20 2023 04:35:10

%S 216,432,648,1000,1080,1296,1512,2000,2160,2376,2744,2808,3000,3024,

%T 3240,3375,3672,4104,4536,4752,4968,5000,5488,5616,6000,6264,6480,

%U 6696,6750,7000,7128,7344,7560,7776,7992,8208,8232,8424,8856,9072,9261,9288,9936,10000

%N Numbers k such that Sum_{d|k, d = 1 or not a perfect power} mu(k/d) is greater than 1 in absolute value.

%C The numbers of terms not exceeding 10^k, for k = 3, 4, ..., are 4, 44, 427, 4264, 42590, 425566, 4255231, 42550413, ... . Apparently, the asymptotic density of this sequence exists and equals 0.00425... . - _Amiram Eldar_, May 20 2023

%H Andrew Howroyd, <a href="/A304369/b304369.txt">Table of n, a(n) for n = 1..1000</a>

%t Select[Range[10000],Abs[Sum[If[d>1&&GCD@@FactorInteger[d][[All,2]]===1,MoebiusMu[#/d],0],{d,Divisors[#]}]]>1&]

%o (PARI) ok(n)={abs(sumdiv(n, d, if(ispower(d), 0, moebius(n/d)))) > 1} \\ _Andrew Howroyd_, Aug 26 2018

%Y Cf. A000005, A000961, A001221, A001597, A001694, A005117, A007916, A008683, A091050, A304326, A304327, A304362, A304364, A304365.

%K nonn

%O 1,1

%A _Gus Wiseman_, May 11 2018