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Numbers k for which the Mertens function M(k) (A002321) is 1.
7

%I #27 Jan 02 2019 05:33:32

%S 1,94,97,98,99,100,146,147,148,161,162,215,216,230,237,330,334,337,

%T 338,349,350,351,352,365,394,397,399,400,415,416,418,538,539,540,542,

%U 606,794,799,800,801,806,809,810,813,815,816,822,851,852,870,874,875

%N Numbers k for which the Mertens function M(k) (A002321) is 1.

%H Seiichi Manyama, <a href="/A118684/b118684.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MertensFunction.html">Mertens Function</a>

%e M(94) = Sum_{n=1..94} mu(n) = 1.

%t Select[Range[500], Plus @@ MoebiusMu[Range[#]] == 1 &] (* _Carl Najafi_, Aug 17 2011 *)

%o (PARI) isok(n) = sum(k=1, n, moebius(k)) == 1; \\ _Michel Marcus_, Nov 20 2017

%Y Numbers k such that M(k) = b: A171395 (b=-12), A171394 (b=-11), A171393 (b=-10), A171392 (b=-9), A171391 (b=-8), A171383 (b=-7), A171374 (b=-6), A171236 (b=-5), A171235 (b=-4), A171098 (b=-3), A171097 (b=-2), A171096 (b=-1), A028442 (b=0), this sequence (b=1), A171403 (b=2), A171404 (b=3), A171406 (b=4), A171427 (b=5), A171428 (b=6), A171436 (b=7).

%Y Cf. A002321, A051400.

%K nonn

%O 1,2

%A Yoav Kallus (colonelmustard(AT)gmail.com), May 20 2006