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%I #9 Aug 10 2022 08:27:06
%S 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,
%T 13,13,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,14,15,15,15,15,15,
%U 15,15,15,15,15,15,15,15,15,17,17,17,17,17,17,17,17,17,17,17,17,17,17,17
%N Number of distinct Fibonacci divisors of the factorial of n.
%F a(n) = A005086(A000142(n)).
%e 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.
%p 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);
%t ndf[n_]:=Length[Intersection[fibs,Divisors[n!]]]; fibs=Fibonacci[ Range[600]];Array[ndf,75] (* _Harvey P. Dale_, Jun 24 2017 *)
%Y Cf. A005086, A000142, A000045.
%K nonn
%O 1,2
%A _R. J. Mathar_, Oct 31 2007
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