A349565 Dirichlet convolution of Fibonacci numbers with A349452 (Dirichlet inverse of A011782, 2^(n-1)).

1, -1, -2, -3, -11, -16, -51, -93, -214, -419, -935, -1812, -3863, -7649, -15698, -31443, -63939, -127676, -257963, -516037, -1037298, -2076547, -4165647, -8335716, -16702015, -33421217, -66911078, -133875827, -267921227, -535987784, -1072395555, -2145208557, -4291436930, -8584038291, -17170640199, -34344407256

Offset: 1

Author

Antti Karttunen, Nov 22 2021

Keywords

• sign

Comments

Dirichlet convolution of this sequence with A034738 produces A034748.

Links

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

Crossrefs

Cf. A000045, A011782, A349452, A349566 (Dirichlet inverse).

Cf. also A034738, A034748, A349563, A349567, A349569.

Programs

Mathematica

s[1] = 1; s[n_] := s[n] = -DivisorSum[n, s[#] * 2^(n/# - 1) &, # < n &]; a[n_] := DivisorSum[n, Fibonacci[#] * s[n/#] &]; Array[a, 36] (* 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)));
A349565(n) = sumdiv(n,d,fibonacci(d)*A349452(n/d));

Formula

a(n) = Sum_{d|n} A000045(d) * A349452(n/d).