OFFSET
1
COMMENTS
According to the formula in A048691, n is coprime to 6 if the exponents in the canonical prime factorization of n are a subset of A007494, i.e., none of the exponents is in A016777. An immediate consequence is that a(n)=|A307424(n)| is true. - R. J. Mathar, Feb 07 2023
LINKS
FORMULA
Multiplicative with a(p^e) = [gcd(2*e+1,6) == 1], where [ ] is the Iverson bracket.
a(n) = abs(A307424(n)). [conjectured]
Dirichlet g.f.: zeta(2*s) * zeta(3*s) / zeta(4*s). - Vaclav Kotesovec, Jul 15 2022
Sum_{k=1..n} a(k) ~ c * sqrt(n), where c = zeta(3/2)/zeta(2) = 1.5881337746... . - Amiram Eldar, Oct 05 2023
MATHEMATICA
Table[If[CoprimeQ[DivisorSigma[0, n^2], 6], 1, 0], {n, 1, 100}] (* Vaclav Kotesovec, Jul 14 2022 *)
PROG
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Antti Karttunen, Jul 13 2022
STATUS
approved