

A335130


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


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
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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: A099033 A187786 A002330 * A305900 A287943 A305211
Adjacent sequences: A335127 A335128 A335129 * A335131 A335132 A335133


KEYWORD

nonn


AUTHOR

Mats Granvik, May 24 2020


STATUS

approved



