A379115 a(n) = A328845(n) mod 5, where A328845 is the first Fibonacci based variant of arithmetic derivative.

0, 0, 1, 2, 4, 0, 2, 3, 2, 2, 0, 4, 0, 3, 3, 0, 2, 2, 3, 1, 0, 3, 4, 2, 2, 0, 4, 4, 0, 4, 0, 4, 0, 4, 1, 0, 4, 2, 1, 0, 0, 1, 2, 2, 0, 0, 2, 3, 3, 2, 0, 0, 4, 3, 0, 0, 3, 1, 2, 1, 0, 1, 4, 1, 2, 0, 1, 3, 1, 2, 0, 4, 4, 3, 1, 0, 0, 1, 4, 1, 0, 1, 3, 2, 1, 0, 2, 0, 4, 4, 0, 0, 0, 4, 3, 0, 4, 2, 3, 3, 0, 1, 1, 2, 0, 0

Offset: 0

Author

Antti Karttunen, Dec 15 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..81839

Crossrefs

Cf. A010874, A328845, A374125, A374205, A379116 (positions of 0's), A379117 (their characteristic function).

Programs

Mathematica

A379115[n_] := If[n <= 1, 0, Mod[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 5]];
Array[A379115, 100, 0] (* Paolo Xausa, Dec 16 2024 *)

PARI

A379115(n) = if(n<=1, 0, my(f=factor(n)); (n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1]))%5);

Formula

a(n) = A010874(A328845(n)) = A010874(A374125(n)).