A132125 Number of distinct Fibonacci divisors of the factorial of n.

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

Links

Table of n, a(n) for n=1..75.

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

Cf. A005086, A000142, A000045.

Sequence in context: A323633 A363275 A291567 * A102672 A287643 A114955

Adjacent sequences: A132122 A132123 A132124 * A132126 A132127 A132128

Keyword

nonn

Author

R. J. Mathar, Oct 31 2007

Status

approved