login
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).
11
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.
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. also A353494, A368994.
Sequence in context: A015703 A015582 A100910 * A359605 A368994 A217096
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 14 2024
STATUS
approved