A374036 a(n) = 1 if A328845(n) and A328846(n) are both even, otherwise 0, where A328845 and A328846 are the first and second Fibonacci-based variants of the arithmetic derivative.

1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 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, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0, 0, 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) = A374045(n) * A374048(n).

a(n) = A059841(A374035(n)).

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]));
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]));
A374036(n) = (!(A328845(n)%2) && !(A328846(n)%2));

Crossrefs

Characteristic function of A374037, whose complement A374038 gives the indices of 0's.

Cf. A000045, A000720, A059841, A328845, A328846, A374035, A374045, A374048.

Sequence in context: A353494 A190610 A095901 * A087049 A358680 A186447

Adjacent sequences: A374033 A374034 A374035 * A374037 A374038 A374039

Keyword

nonn

Author

Antti Karttunen, Jun 28 2024

Status

approved