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

0,4

Links

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

Formula

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

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 *)

Prog

(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);

Crossrefs

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

Sequence in context: A011165 A188672 A228518 * A279647 A028963 A004516

Adjacent sequences: A379112 A379113 A379114 * A379116 A379117 A379118

Keyword

nonn,new

Author

Antti Karttunen, Dec 15 2024

Status

approved