login
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.
9
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.
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. also A369001, A369004, A369653.
Sequence in context: A015087 A082784 A373474 * A105165 A058342 A205808
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 28 2024
STATUS
approved