A373493 a(n) = 1 if A059975(n) and A003415(n) are both multiples of 3, otherwise 0, where A059975 is fully additive with a(p) = p-1, and A003415 is the arithmetic derivative.

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

Offset

1

Links

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for characteristic functions

Formula

a(n) = [A373378(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

a(n) >= A373491(n).

Prog

(PARI)
A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A059975(n) = {my(f = factor(n)); sum(i = 1, #f~, f[i, 2]*(f[i, 1] - 1)); };
A373493(n) = (!(A059975(n)%3) && !(A003415(n)%3));

Crossrefs

Characteristic function of A373494.

Cf. A003415, A059975, A373378, A373491.

Sequence in context: A373588 A373596 A373472 * A014646 A015283 A014548

Adjacent sequences: A373490 A373491 A373492 * A373494 A373495 A373496

Keyword

nonn

Author

Antti Karttunen, Jun 10 2024

Status

approved