A304364 Numbers k such that A304362(k) = Sum_{d|k, d = 1 or not a perfect power} mu(k/d) = 0.

2, 3, 5, 6, 7, 8, 10, 11, 13, 14, 15, 16, 17, 19, 21, 22, 23, 24, 26, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 40, 41, 42, 43, 46, 47, 48, 51, 53, 54, 55, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 69, 70, 71, 73, 74, 77, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88

Offset: 1

Author

Gus Wiseman, May 11 2018

Keywords

• nonn

Comments

Also numbers k such that mu(k) = -Sum_{d|k, d not a perfect power} mu(k/d).

Contains all squarefree numbers (A005117) except 1.

The numbers of terms not exceeding 10^k, for k = 1, 2, ..., are 7, 74, 746, 7443, 74337, 743235, 7432161, 74320977, 743208896, 7432087549, ... . Apparently, the asymptotic density of this sequence exists and equals 0.743208... . - 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, A304365, 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