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

1,1

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.

Formula

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

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}]

Crossrefs

Cf. A334312.

Sequence in context: A187786 A002330 A374211 * A373595 A358747 A373251

Adjacent sequences: A335127 A335128 A335129 * A335131 A335132 A335133

Keyword

nonn

Author

Mats Granvik, May 24 2020

Status

approved