%I #18 Sep 12 2021 12:45:09

%S 0,1,1,1,1,1,1,1,2,1,1,2,1,2,1,1,2,2,2,2,1,3,1,1,2,1,2,1,2,3,1,2,2,2,

%T 4,1,3,2,3,2,2,3,2,1,2,1,2,3,4,1,1,2,2,2,2,6,3,2,2,2,1,5,3,3,2,2,2,1,

%U 4,3,1,2,6,2,2,1,5,2,1,2,2,1,2,1,4,2,1,4,3,9,2,2,4

%N Shadow transform of Fibonacci numbers.

%H Lorenz Halbeisen and Norbert Hungerbuehler, <a href="http://nntdm.net/volume-05-1999/number-4/138-150/">Number theoretic aspects of a combinatorial function</a>, Notes on Number Theory and Discrete Mathematics 5(4) (1999), 138-150. See Definition 7 for the shadow transform.

%H OEIS Wiki, <a href="/wiki/Shadow_transform">Shadow transform</a>.

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>.

%p a:= n-> add(`if`(modp(combinat[fibonacci](j), n)=0, 1, 0), j=0..n-1):

%p seq(a(n), n=0..100); # _Alois P. Heinz_, Jul 04 2021

%t a[n_] := Sum[Boole @ Divisible[Fibonacci[i], n], {i, 0, n - 1}]; Array[a, 100, 0] (* _Amiram Eldar_, Jul 13 2021 *)

%o (Python)

%o from sympy import fibonacci

%o def a(n): return n - sum(fibonacci(k)%n != 0 for k in range(n))

%o print([a(n) for n in range(93)]) # _Michael S. Branicky_, Jul 04 2021

%o (PARI) a(n) = n - sum(k=0, n-1, sign(fibonacci(k)% n)); \\ _Michel Marcus_, Jul 04 2021

%Y Cf. A000045 (Fibonacci numbers).

%K nonn

%O 0,9

%A _Wesley Ivan Hurt_, Jul 04 2021