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A349565
Dirichlet convolution of Fibonacci numbers with A349452 (Dirichlet inverse of A011782, 2^(n-1)).
6
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
1,3
COMMENTS
Dirichlet convolution of this sequence with A034738 produces A034748.
LINKS
FORMULA
a(n) = Sum_{d|n} A000045(d) * A349452(n/d).
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 *)
PROG
(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(d<n, A011782(n/d)*A349452(d), 0)); mapput(memoA349452, n, v); (v)));
A349565(n) = sumdiv(n, d, fibonacci(d)*A349452(n/d));
CROSSREFS
Cf. A000045, A011782, A349452, A349566 (Dirichlet inverse).
Sequence in context: A228520 A361127 A280969 * A091734 A373197 A341784
KEYWORD
sign
AUTHOR
Antti Karttunen, Nov 22 2021
STATUS
approved