

A335138


a(n) = 1 + Sum_{k=1..2*n} sign((sign(n+Sum_{j=2..k}A309229(n,j))+1)).


2



3, 5, 5, 5, 6, 7, 9, 10, 7, 11, 8, 13, 8, 15, 12, 11, 10, 11, 11, 13, 13, 14, 13, 14, 13, 15, 14, 15, 13, 19, 17, 17, 17, 19, 16, 19, 15, 14, 17, 17, 15, 22, 17, 23, 20, 19, 17, 19, 17, 19, 19, 21, 19, 21, 19, 21, 21, 21, 21, 23, 22, 22, 22, 19, 21, 23, 23, 23
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OFFSET

1,1


COMMENTS

a(n) appears to be asymptotic to sqrt(8*n). Taken from the comment by Lekraj Beedassy in A003418: "An assertion equivalent to the Riemann hypothesis is:
 Sum_{k>=1} (A309229(n, k)/k  1/k)  n  < sqrt(n) * log(n)^2."


LINKS

Table of n, a(n) for n=1..68.


FORMULA

a(n) = 1 + Sum_{k=1..2*n} sign((sign(n+Sum_{j=2..k}A309229(n,j))+1)).


MATHEMATICA

nn = 68; f[n_] := n; h[n_] := DivisorSum[n, MoebiusMu[#] # &]; A = Accumulate[Table[Table[h[GCD[n, k]], {k, 1, nn}], {n, 1, nn}]]; B = Abs[A]; B[[All, 1]] = Table[f[n], {n, 1, nn}]; b = 1 + Total[Sign[1 + Sign[Accumulate[Transpose[B]]]]]


CROSSREFS

Cf. A309229.
Sequence in context: A016658 A331210 A330874 * A196604 A131506 A113722
Adjacent sequences: A335135 A335136 A335137 * A335139 A335140 A335141


KEYWORD

nonn


AUTHOR

Mats Granvik, Jun 09 2020


STATUS

approved



