A028442 Numbers k such that Mertens's function M(k) (A002321) is zero.

2, 39, 40, 58, 65, 93, 101, 145, 149, 150, 159, 160, 163, 164, 166, 214, 231, 232, 235, 236, 238, 254, 329, 331, 332, 333, 353, 355, 356, 358, 362, 363, 364, 366, 393, 401, 403, 404, 405, 407, 408, 413, 414, 419, 420, 422, 423, 424, 425, 427

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000 (terms 1..5361 from T. D. Noe)
• Eric Weisstein's World of Mathematics, Mertens Function.

Crossrefs

Cf. A002321, A118684, A171096.

Programs

Magma

M := func; [n: n in [1..500] | M(n) eq 0]; // Bruno Berselli, Jul 12 2021

Mathematica

Select[Range[500], Plus@@MoebiusMu[Range[#]] == 0 &] (* Alonso del Arte, Jul 06 2004 *)
seq[kmax_] := Position[Accumulate[MoebiusMu[Range[kmax]]], 0] // Flatten; seq[500] (* Amiram Eldar, Jun 09 2024 *)

PARI

isok(n) = sum(k=1, n, moebius(k)) == 0; \\ Michel Marcus, Nov 20 2017

PARI

lista(kmax) = {my(s = 0); for(k = 1, kmax, s += moebius(k); if(s == 0, print1(k, ", ")));} \\ Amiram Eldar, Jun 09 2024

Perl

use ntheory ":all"; for (moebius(1,1e7)) { ++$i; say $i unless $M+=$; } # _Dana Jacobsen, May 22 2015