This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A198259 #26 May 24 2025 02:42:10
%S A198259 0,0,1,1,3,2,6,5,9,9,17,13,26,26,39,39,66,61,104,102,156,162,265,249,
%T A198259 405,419,646,652,1059,1031,1676,1696,2660,2705,4362,4283,6937,7039,
%U A198259 11159,11206,18138,17998,29130,29325,46805,47075,76171,75713,122502,123123
%N A198259 a(n) = Sum_{k=1..n} F(n mod k) where F = A000045, the Fibonacci numbers.
%H A198259 Reinhard Zumkeller, <a href="/A198259/b198259.txt">Table of n, a(n) for n = 1..1000</a>
%H A198259 Benoit Cloitre, <a href="http://BCmathematics.monsite-orange.fr/Asymptotic%20sum%202%5E(n%20mod%20k).pdf">An asymptotic formula for sum_{k=1..n}x^(n modk)</a> [broken link]
%F A198259 a(n) is asymptotic to (1/10)*(5+sqrt(5))*phi^ceiling(n/2) where phi = (1+sqrt(5))/2.
%t A198259 a[n_] := Sum[Fibonacci[Mod[n, k]], {k, 1, n}]; Array[a, 50] (* _Amiram Eldar_, May 24 2025 *)
%o A198259 (Haskell)
%o A198259 a198259 n = sum $ map (a000045 . (mod n)) [1..n]
%o A198259 -- _Reinhard Zumkeller_, Oct 22 2011
%Y A198259 Cf. A000045, A001622.
%K A198259 nonn
%O A198259 1,5
%A A198259 _Benoit Cloitre_, Oct 22 2011