The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A349565 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A349565

Dirichlet convolution of Fibonacci numbers with A349452 (Dirichlet inverse of A011782, 2^(n-1)).
(history; published version)

#11 by N. J. A. Sloane at Thu Nov 25 12:15:31 EST 2021

STATUS

reviewed

approved

#10 by Michel Marcus at Thu Nov 25 02:30:32 EST 2021

STATUS

proposed

reviewed

#9 by Antti Karttunen at Thu Nov 25 01:32:04 EST 2021

STATUS

editing

proposed

#8 by Antti Karttunen at Thu Nov 25 01:17:33 EST 2021

LINKS

Antti Karttunen, <a href="/A349565/b349565.txt">Table of n, a(n) for n = 1..1001</a>

STATUS

approved

editing

#7 by Susanna Cuyler at Mon Nov 22 19:58:31 EST 2021

STATUS

proposed

approved

#6 by Amiram Eldar at Mon Nov 22 11:40:46 EST 2021

STATUS

editing

proposed

#5 by Amiram Eldar at Mon Nov 22 11:40:42 EST 2021

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 *)

STATUS

proposed

editing

#4 by Antti Karttunen at Mon Nov 22 11:13:02 EST 2021

STATUS

editing

proposed

#3 by Antti Karttunen at Mon Nov 22 09:37:27 EST 2021

CROSSREFS

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

#2 by Antti Karttunen at Mon Nov 22 09:31:39 EST 2021

NAME

allocated for Antti KarttunenDirichlet convolution of Fibonacci numbers with A349452 (Dirichlet inverse of A011782, 2^(n-1)).

DATA

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.

FORMULA

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

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,

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

KEYWORD

allocated

sign

AUTHOR

Antti Karttunen, Nov 22 2021

STATUS

approved

editing