A369643 a(n) = 1 if n' / gcd(n,n') is a multiple of 3, otherwise 0. Here n' stands for the arithmetic derivative of n, A003415.

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

Offset

1

Comments

a(n) = 1 if numerator of Sum(e/p: n=Product(p^e)) is of the form 3k, and 0 if it is not.

Question: Does this sequence have an asymptotic mean? Partial sums for range [1..10^n-1], for n=1..10 are: 2, 19, 208, 2196, 22346, 225544, 2267048, 22752664, 228098405, 2285194569.

Links

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

Index entries for characteristic functions

Formula

a(n) = A079978(A083345(n)).

a(n) = [A083345(n) == 0 (mod 3)], where [ ] is the Iverson bracket.

a(n) <= A359430(n).

Prog

(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369643(n) = !(A083345(n)%3);

Crossrefs

Characteristic function of A369644.

Cf. A079978, A083345, A359430.

Cf. also A369001, A369004, A369653.

Sequence in context: A015087 A082784 A373474 * A105165 A058342 A205808

Adjacent sequences: A369640 A369641 A369642 * A369644 A369645 A369646

Keyword

nonn

Author

Antti Karttunen, Jan 28 2024

Status

approved