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A304364
Numbers k such that A304362(k) = Sum_{d|k, d = 1 or not a perfect power} mu(k/d) = 0.
5
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
1,1
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
MATHEMATICA
Select[Range[100], Sum[If[GCD@@FactorInteger[d][[All, 2]]===1, MoebiusMu[#/d], 0], {d, Divisors[#]}]===0&]
PROG
(PARI) ok(n)={sumdiv(n, d, if(ispower(d), 0, moebius(n/d))) == 0} \\ Andrew Howroyd, Aug 26 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 11 2018
STATUS
approved