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A132125
Number of distinct Fibonacci divisors of the factorial of n.
0
1, 2, 3, 4, 5, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17
OFFSET
1,2
FORMULA
a(n) = A005086(A000142(n)).
EXAMPLE
a(8)=7 because 8!=40320=2^7*3^2*5*7 has the seven divisors 1, 2, 3, 5, 8, 21 and 144 which are also Fibonacci numbers.
MAPLE
A005086 := proc(n) local a, i, f; a := 0 ; for i from 2 do f := combinat[fibonacci](i) ; if f > n then RETURN(a) ; fi ; if n mod f = 0 then a := a+1 ; fi ; od: end: A000142 := proc(n) n! ; end: A := proc(n) A005086(A000142(n)) ; end: seq(A(n), n=1..80);
MATHEMATICA
ndf[n_]:=Length[Intersection[fibs, Divisors[n!]]]; fibs=Fibonacci[ Range[600]]; Array[ndf, 75] (* Harvey P. Dale, Jun 24 2017 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
R. J. Mathar, Oct 31 2007
STATUS
approved