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

Author

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

Keywords

• nonn
• nice

Comments

Related to the Riemann Hypothesis through the Titchmarsh Theorem.

Examples

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

Crossrefs

Essentially same as A051402 except for initial terms.

Programs

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 *)