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.

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

Andrew Howroyd, Table of n, a(n) for n = 1..1000

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

Crossrefs

Cf. A000005, A000961, A001221, A001597, A001694, A005117, A007916, A008683, A091050, A304326, A304327, A304362, A304364, A304365.

Sequence in context: A327284 A372695 A043371 * A074266 A208089 A333316

Adjacent sequences: A304366 A304367 A304368 * A304370 A304371 A304372

Keyword

nonn

Author

Gus Wiseman, May 11 2018

Status

approved