A349567 Dirichlet convolution of A133494 [3^(n-1)] with A349452 (Dirichlet inverse of A011782, 2^(n-1)).

1, 1, 5, 17, 65, 197, 665, 2017, 6285, 19025, 58025, 174565, 527345, 1584737, 4766245, 14311841, 42981185, 128995317, 387158345, 1161697825, 3485732845, 10458138977, 31376865305, 94134428213, 282412758225, 847253996225, 2541798693045, 7625460083185, 22876524019505, 68629830861205, 205890058352825, 617671220125537

Offset: 1

Author

Antti Karttunen, Nov 22 2021

Keywords

• nonn

Comments

Dirichlet convolution of this sequence with A034738 produces A034754.

Links

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

Crossrefs

Cf. A011782, A133494, A349452, A349568 (Dirichlet inverse).

Cf. also A034738, A034754, A349563, A349565, A349569.

Programs

Mathematica

s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 2^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, 3^(# - 1) * s[n/#] &]; Array[a, 32] (* Amiram Eldar, Nov 22 2021 *)

PARI

A011782(n) = (2^(n-1));
memoA349452 = Map();
A349452(n) = if(1==n,1,my(v); if(mapisdefined(memoA349452,n,&v), v, v = -sumdiv(n,d,if(dA011782(n/d)*A349452(d),0)); mapput(memoA349452,n,v); (v)));
A349567(n) = sumdiv(n,d,(3^(d-1)) * A349452(n/d));

Formula

a(n) = Sum_{d|n} 3^(d-1) * A349452(n/d).