A119936 Least common multiple (LCM) of denominators of the rows of the triangle of rationals A119935/A119932.

1, 8, 108, 576, 18000, 21600, 1234800, 5644800, 57153600, 63504000, 8452382400, 9220780800, 1688171284800, 1818030614400, 1947889944000, 8310997094400, 2551995545299200, 2702112930316800, 1029655143835718400

Offset: 1

Author

Wolfdieter Lang, Jul 20 2006

Keywords

• nonn
• easy

Comments

The triangle of rationals is the matrix cube of the matrix with elements a(i,j) = 1/i if j <= i, 0 if j > i.

Links

• Stephen Crowley, Two New Zeta Constants: Fractal String, Continued Fraction, and Hypergeometric Aspects of the Riemann Zeta Function, arXiv:1207.1126 [math.NT], 2012.

Crossrefs

Distinct from A246498.

Formula

A027447(i,j)= a(i)* A119935(i,j)/A119932(i,j) .

a(n) = lcm_{m=1..n} seq(A119932(n,m)), n >= 1.

a(n)/n^3 = A027451(n) = A002944(n)^2 (the second equation is a conjecture).

a(n)/n^3 = (A099946(n)*(n-1))^2, n >= 2 (from the conjecture).