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

1,1

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.

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 *)

Prog

(Perl) use ntheory ":all"; for (moebius(1, 1e7)) { ++$i; say $i unless $M+=$_; } # Dana Jacobsen, May 22 2015
(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
(Magma) M := func<i | &+[MoebiusMu(k): k in [1..i]]>; [n: n in [1..500] | M(n) eq 0]; // Bruno Berselli, Jul 12 2021

Crossrefs

Cf. A002321, A118684, A171096.

Sequence in context: A066244 A055689 A345316 * A062982 A042801 A078733

Adjacent sequences: A028439 A028440 A028441 * A028443 A028444 A028445

Keyword

nonn,changed

Author

Eric W. Weisstein

Status

approved