A374202 The 2-adic valuation of A328845(n), where A328845 is a Fibonacci-based variant of the arithmetic derivative.

0, 1, 2, 0, 0, 0, 2, 2, 0, 0, 2, 0, 0, 0, 5, 0, 0, 0, 3, 0, 0, 0, 2, 1, 0, 1, 4, 0, 0, 0, 4, 0, 0, 2, 2, 0, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 7, 1, 0, 0, 3, 0, 0, 2, 2, 0, 0, 0, 5, 0, 0, 0, 6, 1, 0, 0, 3, 0, 0, 0, 2, 0, 0, 3, 5, 1, 0, 0, 4, 3, 0, 0, 3, 1, 0, 0, 2, 0, 0, 3, 5, 0, 0, 3, 4, 0, 0, 0, 2, 0, 0, 0, 2, 1, 0, 0, 2

Offset

2,3

Links

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

Formula

a(n) = A007814(A328845(n)).

Mathematica

A374202[n_] := IntegerExponent[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 2];
Array[A374202, 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]));
A374202(n) = valuation(A328845(n), 2);

Crossrefs

Cf. A007814, A328845, A374045, A374046 (after its 2 initial terms, gives the indices of nonzero terms in this sequence), A374047 (indices of 0's).

Cf. also A374132, A374212, A374203, A374205.

Sequence in context: A369309 A216228 A372602 * A291957 A143063 A210703

Adjacent sequences: A374199 A374200 A374201 * A374203 A374204 A374205

Keyword

nonn,changed

Author

Antti Karttunen, Jul 01 2024

Status

approved