A369004 a(n) = 1 if n' / gcd(n,n') is a multiple of 4, otherwise 0, where n' stands for the arithmetic derivative of n, A003415(n).

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

Offset

1

Comments

a(n) = 1 if A083345(n) = the numerator of Sum(e/p: n=Product(p^e)) is of the form 4k, and 0 if it is not.

Question: Is the asymptotic mean of this sequence 1/6? See also A369001.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for characteristic functions

Formula

a(n) = A121262(A083345(n)).

a(n) <= A369001(n).

a(n) <= A368994(n) <= A353494(n).

a(n) <= 1 - A369006(n).

Prog

(PARI)
A083345(n) = { my(f=factor(n)); numerator(vecsum(vector(#f~, i, f[i, 2]/f[i, 1]))); };
A369004(n) = !(A083345(n)%4);

Crossrefs

Characteristic function of A369005.

Cf. A083345, A121262, A369001, A369006.

Cf. also A353494, A368994.

Sequence in context: A015703 A015582 A100910 * A359605 A368994 A217096

Adjacent sequences: A369001 A369002 A369003 * A369005 A369006 A369007

Keyword

nonn

Author

Antti Karttunen, Jan 14 2024

Status

approved