A374117 a(n) = 1 if A328768(n) and A328845(n) are both multiples of 3, otherwise 0, where A328768 is the first primorial based variant and A328845 is the first Fibonacci-based variant of the arithmetic derivative, respectively.

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

Offset

0

Links

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

Index entries for characteristic functions

Formula

a(n) = A079978(A374116(n)).

a(n) = A373991(n) * A374121(n).

Prog

(PARI)
A002110(n) = prod(i=1, n, prime(i));
A328768(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]*A002110(primepi(f[i, 1])-1)/f[i, 1]));
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]));
A374117(n) = (!(A328768(n)%3) && !(A328845(n)%3));

Crossrefs

Characteristic function of A374118.

Cf. A079978, A328768, A328845, A373991, A374121, A374116.

Sequence in context: A353566 A279484 A279329 * A359430 A374121 A292438

Adjacent sequences: A374114 A374115 A374116 * A374118 A374119 A374120

Keyword

nonn

Author

Antti Karttunen, Jul 08 2024

Status

approved