A349568 Dirichlet convolution of A011782 [2^(n-1)] with A349453 (Dirichlet inverse of A133494, 3^(n-1)).

1, -1, -5, -16, -65, -187, -665, -1984, -6260, -18895, -58025, -174016, -527345, -1583407, -4765595, -14307568, -42981185, -128980852, -387158345, -1161657760, -3485726195, -10458022927, -31376865305, -94134053296, -282412754000, -847252941535, -2541798630320, -7625456893096, -22876524019505, -68629821114805

Offset: 1

Author

Antti Karttunen, Nov 22 2021

Keywords

• sign

Comments

Dirichlet convolution of this sequence with A034754 produces A034738.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1001

Crossrefs

Cf. A011782, A133494, A349453, A349567 (Dirichlet inverse).

Cf. also A034738, A034754, A349564, A349566, A349570.

Programs

Mathematica

s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 3^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, 2^(# - 1) * s[n/#] &]; Array[a, 30] (* Amiram Eldar, Nov 22 2021 *)

PARI

A133494(n) = max(1, 3^(n-1));
memoA349453 = Map();
A349453(n) = if(1==n,1,my(v); if(mapisdefined(memoA349453,n,&v), v, v = -sumdiv(n,d,if(dA133494(n/d)*A349453(d),0)); mapput(memoA349453,n,v); (v)));
A349568(n) = sumdiv(n,d,(2^(d-1)) * A349453(n/d));

Formula

a(n) = Sum_{d|n} 2^(d-1) * A349453(n/d).