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

1, 4, 9, 12, 18, 20, 25, 28, 36, 44, 45, 49, 50, 52, 60, 63, 68, 72, 75, 76, 84, 90, 92, 98, 99, 100, 108, 116, 117, 121, 124, 126, 132, 140, 144, 147, 148, 150, 153, 156, 164, 169, 171, 172, 175, 180, 188, 196, 198, 200, 204, 207, 212, 216, 220, 225, 228, 234

Offset: 1

Author

Gus Wiseman, May 11 2018

Keywords

• nonn

Comments

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

Contains all prime powers (A000961).

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

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, A304369.

Programs

Mathematica

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

PARI

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