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

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, 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, 10, 174, 1, 14, 3051, 69, 10, 5, 1, 39

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 (terms 1..100 from Indranil Ghosh)

Crossrefs

Cf. A000045, A005092.

Programs

Mathematica

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 *)

Python

from sympy import divisors, fibonacci
l = [fibonacci(n) for n in range(1, 21)]
def a(n):
    return sum(i**2 for i in divisors(n) if i in l)
print([a(n) for n in range(1, 101)])  # Indranil Ghosh, Mar 22 2017

Formula

G.f.: Sum_{k>=2} Fibonacci(k)^2*x^Fibonacci(k)/(1 - x^Fibonacci(k)). - Ilya Gutkovskiy, Mar 21 2017

Extensions

Offset changed from 0 to 1 by Ilya Gutkovskiy, Mar 21 2017

b-file corrected by Vaclav Kotesovec, Apr 29 2019