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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.
4
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
1,1
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
MATHEMATICA
Select[Range[10000], Abs[Sum[If[d>1&&GCD@@FactorInteger[d][[All, 2]]===1, MoebiusMu[#/d], 0], {d, Divisors[#]}]]>1&]
PROG
(PARI) ok(n)={abs(sumdiv(n, d, if(ispower(d), 0, moebius(n/d)))) > 1} \\ Andrew Howroyd, Aug 26 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, May 11 2018
STATUS
approved