A374205 The 5-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.

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

Offset: 2

Author

Antti Karttunen, Jul 01 2024

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 2..100000

Crossrefs

Cf. A000045, A112765, A328845.

Cf. also A374133, A374213, A374202.

Programs

Mathematica

A374205[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 5];
Array[A374205, 100, 2] (* Paolo Xausa, Dec 16 2024 *)

PARI

A328845(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(f[i,1])/f[i, 1]));
A374205(n) = valuation(A328845(n), 5);

Formula

a(n) = A112765(A328845(n)).