A349433 a(n) = A349431(n) + A349432(n).

2, 0, 0, 1, 0, 2, 0, 3, 1, 4, 0, 3, 0, 6, 4, 7, 0, 3, 0, 6, 6, 10, 0, 5, 4, 12, 3, 9, 0, -4, 0, 15, 10, 16, 12, 5, 0, 18, 12, 10, 0, -6, 0, 15, 2, 22, 0, 9, 9, 8, 16, 18, 0, 5, 20, 15, 18, 28, 0, -4, 0, 30, 3, 31, 24, -10, 0, 24, 22, -12, 0, 9, 0, 36, 0, 27, 30, -12, 0, 18, 7, 40, 0, -6, 32, 42, 28, 25, 0, -6, 36, 33

Offset: 1

Author

Antti Karttunen, Nov 17 2021

Keywords

• sign
• look

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A349431, A349432.

Cf. also A349446.

Programs

Mathematica

k[n_] := (n / 2^IntegerExponent[n, 2] + 1)/2; kinv[1] = 1; kinv[n_] := kinv[n] = -DivisorSum[n, kinv[#] * k[n/#] &, # < n &]; a[n_] := DivisorSum[n, # * kinv[n/#] + # * MoebiusMu[#] * k[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)

PARI

A349433(n) = (A349431(n) + A349432(n)); \\ Needs also code from A349431 and A349432.

Formula

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A349431(d) * A349432(n/d). [As the sequences are Dirichlet inverses of each other]