A349439 a(n) = A349437(n) + A349438(n).

2, 0, 0, 1, 0, 2, 0, 1, 1, 4, 0, -1, 0, 4, 4, 1, 0, 3, 0, -2, 4, 8, 0, -2, 4, 4, 5, -2, 0, -8, 0, 1, 8, 8, 8, -4, 0, 4, 4, -4, 0, -8, 0, -4, 10, 8, 0, -3, 4, 8, 8, -2, 0, 2, 16, -4, 4, 12, 0, -6, 0, 4, 10, 1, 8, -16, 0, -4, 8, -16, 0, -6, 0, 12, 16, -2, 16, -8, 0, -6, 19, 8, 0, -6, 16, 4, 12, -8, 0, -24, 8, -4, 4

Offset: 1

Author

Antti Karttunen, Nov 18 2021

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A349437, A349438.

Programs

Mathematica

f[p_, e_] := NextPrime[p, -1]^e; s[1] = 1; s[n_] := If[EvenQ[n], n/2, Times @@ f @@@ FactorInteger[n]]; sinv[1] = 1; sinv[n_] := sinv[n] = -DivisorSum[n, sinv[#] * s[n/#] &, # < n &]; a[n_] := DivisorSum[n, # * MoebiusMu[#] * s[n/#] + # * sinv[n/#] &]; Array[a, 100] (* Amiram Eldar, Nov 18 2021 *)

PARI

A349439(n) = (A349437(n)+A349438(n)); \\ Needs also code from A349437 and A349438.

Formula

a(1) = 2, and for n >1, a(n) = -Sum_{d|n, 1A349437(d) * A349438(n/d). [As the sequences are Dirichlet inverses of each other]