A264389 Denominator of binomial(n-1, 2)/(6*n), for n >= 1. Denominator of Dedekind sum s(1,n).

1, 1, 18, 8, 5, 18, 14, 16, 27, 5, 22, 72, 13, 14, 90, 32, 17, 27, 38, 40, 63, 22, 46, 144, 25, 13, 162, 56, 29, 90, 62, 64, 99, 17, 70, 216, 37, 38, 234, 80, 41, 63, 86, 88, 135, 46, 94, 288, 49, 25, 306, 104, 53, 162, 110, 112, 171, 29, 118, 360, 61, 62, 378

Offset: 1

Author

Wolfdieter Lang, Jan 11 2016

Keywords

• nonn
• easy
• frac

Comments

See A264388 for the numerators and details about the Dedekind sum s(1,n), as well as references.

Crossrefs

Cf. A264388.

Programs

Julia

using Nemo
A264389(n) = denominator(dedekind_sum(1, n))
[A264389(n) for n in 1:70] |> println # Peter Luschny, Mar 13 2018

Mathematica

Denominator[Table[Binomial[n-1,2]/(6n),{n,50}]] (* Harvey P. Dale, Aug 30 2016 *)

Formula

a(n) = denominator(binomial(n-1, 2)/(6*n)), n >= 1.

a(n) = denominator(s(1,n)), with s(1,n) = Sum_{r=1..(n-1)} (r/n)*(r/n - floor(r/n)- 1/2), n >= 1, where s(h,k) are the Dedekind sums.