cp's OEIS Frontend

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.

A005093 Sum of squares of Fibonacci numbers 1,2,3,5,... that divide n.

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%I A005093 #32 Apr 03 2020 03:38:24
%S A005093 1,5,10,5,26,14,1,69,10,30,1,14,170,5,35,69,1,14,1,30,451,5,1,78,26,
%T A005093 174,10,5,1,39,1,69,10,1161,26,14,1,5,179,94,1,455,1,5,35,5,1,78,1,30,
%U A005093 10,174,1,14,3051,69,10,5,1,39
%N A005093 Sum of squares of Fibonacci numbers 1,2,3,5,... that divide n.
%H A005093 Vaclav Kotesovec, <a href="/A005093/b005093.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..100 from Indranil Ghosh)
%F A005093 G.f.: Sum_{k>=2} Fibonacci(k)^2*x^Fibonacci(k)/(1 - x^Fibonacci(k)). - _Ilya Gutkovskiy_, Mar 21 2017
%t A005093 nmax = 100; With[{fibs = Fibonacci[Range[2, Floor[Log[nmax*Sqrt[5]] / Log[GoldenRatio]] + 1]]}, Table[Total[Select[fibs, Divisible[n, #1] & ]^2], {n, 1, nmax}]] (* _Harvey P. Dale_, Apr 25 2011, fixed by _Vaclav Kotesovec_, Apr 29 2019 *)
%o A005093 (Python)
%o A005093 from sympy import divisors, fibonacci
%o A005093 l = [fibonacci(n) for n in range(1, 21)]
%o A005093 def a(n):
%o A005093     return sum(i**2 for i in divisors(n) if i in l)
%o A005093 print([a(n) for n in range(1, 101)])  # _Indranil Ghosh_, Mar 22 2017
%Y A005093 Cf. A000045, A005092.
%K A005093 nonn
%O A005093 1,2
%A A005093 _N. J. A. Sloane_
%E A005093 Offset changed from 0 to 1 by _Ilya Gutkovskiy_, Mar 21 2017
%E A005093 b-file corrected by _Vaclav Kotesovec_, Apr 29 2019