

A100766


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


4



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
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OFFSET

1,1


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 k1 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


MATHEMATICA

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


CROSSREFS

Cf. A100306, A100765, A100767.
Sequence in context: A160148 A233733 A233726 * A189541 A201233 A135848
Adjacent sequences: A100763 A100764 A100765 * A100767 A100768 A100769


KEYWORD

nonn


AUTHOR

Alonso del Arte, Jan 03 2005


EXTENSIONS

Offset corrected by Donovan Johnson, Jun 19 2012


STATUS

approved



