A374045 a(n) = 1 if A328845(n) is even, otherwise 0, where A328845 is the first Fibonacci based variant of arithmetic derivative.

1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1

Offset

0

Links

Antti Karttunen, Table of n, a(n) for n = 0..100000

Index entries for characteristic functions

Formula

a(n) = A059841(A328845(n)).

Mathematica

A374045[n_] := If[n <= 1, 1, 1 - Mod[n*Total[MapApply[#2*Fibonacci[#]/# &, FactorInteger[n]]], 2]];
Array[A374045, 100, 0] (* 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]));
A374045(n) = !(A328845(n)%2);

Crossrefs

Characteristic function of A374046, whose complement A374047 gives the indices of 0's.

Cf. A000045, A059841, A328845.

Sequence in context: A380667 A089451 A145099 * A205083 A070886 A262808

Adjacent sequences: A374042 A374043 A374044 * A374046 A374047 A374048

Keyword

nonn

Author

Antti Karttunen, Jun 27 2024

Status

approved