A335130 a(n) = 1 + Sum_{k=1..n} sign((sign(n+Sum_{j=2..k}-|A334312(n,j)|)+1)).

2, 3, 4, 5, 6, 5, 7, 7, 10, 7, 11, 10, 11, 10, 11, 11, 14, 13, 14, 13, 13, 11, 15, 12, 17, 13, 17, 13, 19, 13, 14, 15, 15, 15, 17, 17, 17, 19, 19, 17, 19, 17, 18, 17, 17, 18, 21, 19, 22, 21, 21, 19, 21, 21, 23, 23, 19, 19, 26, 19, 19, 23, 23, 23, 29, 21, 22, 21, 23, 21, 23, 22, 23, 23, 28, 23, 31, 23, 26, 25

Offset: 1

Author

Mats Granvik, May 24 2020

Keywords

• nonn

Comments

a(n) appears to be asymptotic to sqrt(8*n).

Links

• Mats Granvik, Table of n, a(n) for n = 1..10000
• Mats Granvik, More efficient Mathematica program for the sequence
• Mats Granvik, Plot of 10000 first terms together with conjectured asymptotic
• Mats Granvik, What is the asymptotic of the irregular blue curve? Is it (8x)^(1/2) or is it something else?, MathOverflow, May 24 2020.

Crossrefs

Cf. A334312.

Programs

Mathematica

nn = 80; varphi[n_] := DivisorSum[n, MoebiusMu[#] # &]; A = Table[Table[Sum[If[n >= k, varphi[GCD[i, k]], 0], {i, k, n}], {k, 1, nn}], {n, 1, nn}]; vv = Table[1 + Sum[Sign[(1 + Sign[Sum[If[j == 1, A[[n, j]], -Abs[A[[n, j]]]], {j, 1, k}]])], {k, 1, n}], {n, 1, nn}]

Formula

a(n) = 1 + Sum_{k=1..n} sign((sign(n+Sum_{j=2..k}-|A334312(n,j)|)+1)).