A374048 a(n) = 1 if A328846(n) is even, otherwise 0, where A328846 is the second Fibonacci based variant of arithmetic derivative.

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

Offset

0

Links

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

Index entries for characteristic functions

Index entries for sequences related to prime indices in the factorization of n

Formula

a(n) = A059841(A328846(n)).

For all n >= 1, a(A000040(n)) = A079978(n-1) = [n == 1 (mod 3)], where [ ] is the Iverson bracket.

Prog

(PARI)
A328846(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*fibonacci(2+primepi(f[i, 1]))/f[i, 1]));
A374048(n) = !(A328846(n)%2);

Crossrefs

Characteristic function of A374049, whose complement A374050 gives the indices of 0's.

Cf. A000040, A000045, A000720, A059841, A079978, A328846.

Cf. also A374045.

Sequence in context: A351957 A342004 A284881 * A090174 A165556 A348292

Adjacent sequences: A374045 A374046 A374047 * A374049 A374050 A374051

Keyword

nonn

Author

Antti Karttunen, Jun 28 2024

Status

approved