A304369 Numbers k such that Sum_{d|k, d = 1 or not a perfect power} mu(k/d) is greater than 1 in absolute value.

216, 432, 648, 1000, 1080, 1296, 1512, 2000, 2160, 2376, 2744, 2808, 3000, 3024, 3240, 3375, 3672, 4104, 4536, 4752, 4968, 5000, 5488, 5616, 6000, 6264, 6480, 6696, 6750, 7000, 7128, 7344, 7560, 7776, 7992, 8208, 8232, 8424, 8856, 9072, 9261, 9288, 9936, 10000

Offset: 1

Author

Gus Wiseman, May 11 2018

Keywords

• nonn

Comments

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

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Mathematica

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

PARI

ok(n)={abs(sumdiv(n, d, if(ispower(d), 0, moebius(n/d)))) > 1} \\ Andrew Howroyd, Aug 26 2018