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An inverse to Mertens's function: smallest k >= 2 such that Mertens's function |M(k)| (see A002321) is equal to n.
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%I #17 Sep 02 2023 15:58:01

%S 2,3,5,13,31,110,114,197,199,443,659,661,665,1105,1106,1109,1637,2769,

%T 2770,2778,2791,2794,2795,2797,2802,2803,6986,6987,7013,7021,8503,

%U 8506,8507,8509,8510,8511,9749,9822,9823,9830,9831,9833,9857,9861,19043

%N An inverse to Mertens's function: smallest k >= 2 such that Mertens's function |M(k)| (see A002321) is equal to n.

%C Related to the Riemann Hypothesis through the Titchmarsh Theorem.

%e M(1637) = 17 because the sum of Moebius mu(1) + mu(2) + ... + mu(1637) = 17.

%p with(numtheory): k := -1: s := 0: for n from 1 to 20000 do s := s+mobius(n): if (abs(s) > k) and (n>1) then k := abs(s): print(n, k); fi; od:

%t Reap[ For[ k = -1; s = 0; n = 1, n <= 20000, n++, s = s + MoebiusMu[n]; If[Abs[s] > k && n > 1, k = Abs[s]; Sow[n]]]][[2, 1]] (* _Jean-François Alcover_, Sep 04 2013, after Maple *)

%Y Essentially same as A051402 except for initial terms.

%K nonn,nice

%O 0,1

%A Luis Rodriguez-Torres (ludovicusmagister(AT)yahoo.com), Apr 06 2001