|
|
A005093
|
|
Sum of squares of Fibonacci numbers 1,2,3,5,... that divide n.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
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)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|