A100766 Numbers for which the values of the Moebius function (A008683) and the Mertens function (A002321) are both 0.

40, 150, 160, 164, 232, 236, 332, 333, 356, 363, 364, 404, 405, 408, 414, 420, 423, 424, 425, 428, 608, 636, 637, 796, 812, 824, 825, 850, 884, 896, 904, 916, 920, 1014, 1220, 1256, 1280, 1292, 1300, 1336, 1492, 1519, 1520, 1521, 1524, 1525, 1528, 1532, 1544

Offset: 1

Author

Alonso del Arte, Jan 03 2005

Keywords

• nonn

Comments

This sequence is a subset of A100306, numbers for which the values of the Moebius function and the Mertens function agree and, in a different way, a subset of A028442, zeros of the Mertens function. There are no prime numbers in this sequence.

Numbers k such that k-1 and k are consecutive zeros of the Mertens function. - Amiram Eldar, Jun 13 2020

Links

• Donovan Johnson, Table of n, a(n) for n = 1..10000
• PrimeFan, Esoteric Integer Sequences
• PrimeFan, Esoteric Integer Sequences [Cached copy]

Crossrefs

Cf. A100306, A100765, A100767.

Programs

Mathematica

(* If not already defined *) If[Names["Mertens"] == {}, Mertens[x_] := Plus @@ MoebiusMu[Range[1, x]]]; Select[Range[2500], MoebiusMu[ # ] == 0 && Mertens[ # ] == 0 &]

Extensions

Offset corrected by Donovan Johnson, Jun 19 2012