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A051402
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Inverse Mertens function: smallest k such that |M(k)| = n, where M(x) is Mertens's function A002321.
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14
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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
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OFFSET
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1,2
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COMMENTS
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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)
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LINKS
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EXAMPLE
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M(31) = -4, smallest one equal to +-4.
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MAPLE
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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:
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MATHEMATICA
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a = s = 0; Do[s = s + MoebiusMu[n]; If[ Abs[s] > a, a = Abs[s]; Print[n]], {n, 1, 20000}]
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PROG
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(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a051402 = (+ 1) . fromJust . (`elemIndex` ms) where
ms = map (abs . a002321) [1..]
(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
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CROSSREFS
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Essentially same as A060434 except for initial terms.
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KEYWORD
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nonn,nice
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AUTHOR
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STATUS
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approved
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