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 A051402 Inverse Mertens function: smallest k such that |M(k)| = n, where M(x) is Mertens's function A002321. 14
 1, 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS From Torlach Rush, Oct 11 2018: (Start) For k <= 10^7: - a(n) is squarefree. - if a(n) > M(k) then A008683(a(n)) is negative. - if a(n) = M(k) then A008683(a(n)) is positive. (End) LINKS T. D. Noe and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from Noe) EXAMPLE M(31) = -4, smallest one equal to +-4. MAPLE with(numtheory): k := 0: s := 0: for n from 1 to 20000 do s := s+mobius(n): if abs(s) > k then k := abs(s): print(n); fi; od: MATHEMATICA a = s = 0; Do[s = s + MoebiusMu[n]; If[ Abs[s] > a, a = Abs[s]; Print[n]], {n, 1, 20000}] PROG (Haskell) import Data.List (elemIndex) import Data.Maybe (fromJust) a051402 = (+ 1) . fromJust . (`elemIndex` ms) where    ms = map (abs . a002321) [1..] -- Reinhard Zumkeller, Dec 26 2012 (PARI) M(n)=sum(k=1, n, moebius(k)); print1(1, ", "); c=M(1); n=2; while(n<10^3, if(abs(M(n))>c, print1(n, ", "); c=abs(M(n))); n++) \\ Derek Orr, Jun 14 2016 (PARI) M(n) = sum(k=1, n, moebius(k)); a(n) = my(k = 1, s = moebius(1)); while (abs(s) != n, k++; s += moebius(k)); k; \\ Michel Marcus, Oct 12 2018 CROSSREFS Cf. A002321, A008683, A051400, A051401. Essentially same as A060434 except for initial terms. Sequence in context: A007708 A146609 A121129 * A147022 A147014 A146376 Adjacent sequences:  A051399 A051400 A051401 * A051403 A051404 A051405 KEYWORD nonn,nice AUTHOR STATUS approved

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Last modified May 22 09:12 EDT 2022. Contains 353941 sequences. (Running on oeis4.)