A349566 Dirichlet convolution of A011782 (2^(n-1)) with A349451 (Dirichlet inverse of Fibonacci numbers).

1, 1, 2, 4, 11, 20, 51, 100, 218, 441, 935, 1862, 3863, 7751, 15742, 31648, 63939, 128180, 257963, 516974, 1037502, 2078417, 4165647, 8339900, 16702136, 33428943, 66911942, 133891584, 267921227, 536021340, 1072395555, 2145272320, 4291440670, 8584166169, 17170641321, 34344672290, 68695318919, 137399603159, 274814652766

Offset: 1

Author

Antti Karttunen, Nov 22 2021

Keywords

• nonn

Comments

Dirichlet convolution of this sequence with A034748 produces A034738.

Links

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

Crossrefs

Cf. A000045, A011782, A349451, A349565 (Dirichlet inverse).

Programs

Mathematica

s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * Fibonacci[n/#] &, # < n &]; a[n_] := DivisorSum[n, 2^(# - 1) * s[n/#] &]; Array[a, 40] (* Amiram Eldar, Nov 22 2021 *)

PARI

memoA349451 = Map();
A349451(n) = if(1==n,1,my(v); if(mapisdefined(memoA349451,n,&v), v, v = -sumdiv(n,d,if(dA349451(d),0)); mapput(memoA349451,n,v); (v)));
A349566(n) = sumdiv(n,d,(2^(d-1)) * A349451(n/d));

Formula

a(n) = Sum_{d|n} 2^(d-1) * A349451(n/d).