A349566 - OEIS

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

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OFFSET

1,3

COMMENTS

Dirichlet convolution of this sequence with A034748 produces A034738.

LINKS

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

FORMULA

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

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 *)

PROG

(PARI)

memoA349451 = Map();

A349451(n) = if(1==n, 1, my(v); if(mapisdefined(memoA349451, n, &v), v, v = -sumdiv(n, d, if(d<n, fibonacci(n/d)*A349451(d), 0)); mapput(memoA349451, n, v); (v)));

A349566(n) = sumdiv(n, d, (2^(d-1)) * A349451(n/d));

CROSSREFS

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

Sequence in context: A076636 A011954 A278446 * A026275 A152597 A320679

Adjacent sequences: A349563 A349564 A349565 * A349567 A349568 A349569

KEYWORD

nonn

AUTHOR

Antti Karttunen, Nov 22 2021

STATUS

approved