A335138 a(n) = 1 + Sum_{k=1..2*n} sign((sign(n+Sum_{j=2..k}-|A309229(n,j)|)+1)).

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

Offset: 1

Author

Mats Granvik, Jun 09 2020

Keywords

• nonn

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."

Crossrefs

Cf. A309229.

Programs

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]]]]]

Formula

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