A242050 Denominator of A242035(n) / A246053(floor(n/2)).

2, 2, 2, 2, 1, 7, 1, 2, 1, 1, 1, 5, 1, 1, 7, 10, 1, 7, 1, 1, 1, 1, 3, 7, 1, 5, 1, 1, 1, 1, 1, 2, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 5, 1, 1, 3, 1, 1, 1, 1, 62, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0,1

Comments

Let h(x) = zeta(2*x)*(4^x-2) and r(n) = h([(n+1)/2])*h([n/2])/ h(n). Then the denominator of r([n/2]) almost divides the numerator of r(n), where 'a almost divides b' means that a divides b or the denominator of the quotient b/a (reduced to lowest terms) is very small compared to the size of b.

Links

Peter Luschny, Table of n, a(n) for n = 0..10000

Example

a(34) = 1 because A246053(17) divides A242035(34).
a(35) = 7 because A242035(35)/A246053(17) = 8416843291197378595121525029762095062482279733/7.

Prog

(Sage)
h = lambda x: zeta(2*x)*(4^x-2)
r = lambda n: h((n+1)//2)*h(n//2)/h(n)
A242050 = lambda n: (r(n).numerator()/r(n//2).denominator()).denominator()
[A242050(n) for n in range(1000)]

Crossrefs

Cf. A242035, A246053.

Sequence in context: A308619 A114294 A371929 * A037869 A037868 A173069

Adjacent sequences: A242047 A242048 A242049 * A242051 A242052 A242053

Keyword

nonn

Author

Peter Luschny, Aug 17 2014

Status

approved