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Numbers for which the values of the Moebius function (A008683) and the Mertens function (A002321) are both 0.
4

%I #17 Jun 13 2020 07:57:23

%S 40,150,160,164,232,236,332,333,356,363,364,404,405,408,414,420,423,

%T 424,425,428,608,636,637,796,812,824,825,850,884,896,904,916,920,1014,

%U 1220,1256,1280,1292,1300,1336,1492,1519,1520,1521,1524,1525,1528,1532,1544

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

%C 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.

%C Numbers k such that k-1 and k are consecutive zeros of the Mertens function. - _Amiram Eldar_, Jun 13 2020

%H Donovan Johnson, <a href="/A100766/b100766.txt">Table of n, a(n) for n = 1..10000</a>

%H PrimeFan, <a href="http://primefan.tripod.com/EsotericIntegerSequences.html">Esoteric Integer Sequences</a>

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

%Y Cf. A100306, A100765, A100767.

%K nonn

%O 1,1

%A _Alonso del Arte_, Jan 03 2005

%E Offset corrected by _Donovan Johnson_, Jun 19 2012