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

2,14

Links

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

Formula

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

Mathematica

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

Prog

(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);

Crossrefs

Cf. A000045, A112765, A328845.

Cf. also A374133, A374213, A374202.

Sequence in context: A083892 A354451 A089814 * A063100 A353377 A294266

Adjacent sequences: A374202 A374203 A374204 * A374206 A374207 A374208

Keyword

nonn,changed

Author

Antti Karttunen, Jul 01 2024

Status

approved