A051402 Inverse Mertens function: smallest k such that |M(k)| = n, where M(x) is Mertens's function A002321.

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

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

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 1000 terms from T. D. 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

Jud McCranie

Status

approved