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

1,2

Links

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

Formula

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

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 *)

Prog

(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

Crossrefs

Cf. A000045, A005092.

Sequence in context: A229793 A285585 A205854 * A328639 A351265 A369718

Adjacent sequences: A005090 A005091 A005092 * A005094 A005095 A005096

Keyword

nonn

Author

N. J. A. Sloane

Extensions

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

b-file corrected by Vaclav Kotesovec, Apr 29 2019

Status

approved