A060434 An inverse to Mertens's function: smallest k >= 2 such that Mertens's function |M(k)| (see A002321) is equal to n.

2, 3, 5, 13, 31, 110, 114, 197, 199, 443, 659, 661, 665, 1105, 1106, 1109, 1637, 2769, 2770, 2778, 2791, 2794, 2795, 2797, 2802, 2803, 6986, 6987, 7013, 7021, 8503, 8506, 8507, 8509, 8510, 8511, 9749, 9822, 9823, 9830, 9831, 9833, 9857, 9861, 19043

Offset

0,1

Comments

Related to the Riemann Hypothesis through the Titchmarsh Theorem.

Links

Table of n, a(n) for n=0..44.

Example

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

Maple

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:

Mathematica

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 *)

Crossrefs

Essentially same as A051402 except for initial terms.

Sequence in context: A167495 A041519 A355512 * A072999 A175093 A342180

Adjacent sequences: A060431 A060432 A060433 * A060435 A060436 A060437

Keyword

nonn,nice

Author

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

Status

approved