|
%I #19 May 20 2023 04:33:51
%S 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,
%T 34,35,37,38,39,40,41,42,43,46,47,48,51,53,54,55,56,57,58,59,61,62,64,
%U 65,66,67,69,70,71,73,74,77,78,79,80,81,82,83,85,86,87,88
%N Numbers k such that A304362(k) = Sum_{d|k, d = 1 or not a perfect power} mu(k/d) = 0.
%C Also numbers k such that mu(k) = -Sum_{d|k, d not a perfect power} mu(k/d).
%C Contains all squarefree numbers (A005117) except 1.
%C 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
%H Andrew Howroyd, <a href="/A304364/b304364.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, A304365, A304369.
%K nonn
%O 1,1
%A _Gus Wiseman_, May 11 2018
|
