A082688 Denominator of Sum_{k=1..n} 1/(n+k).

2, 12, 60, 840, 2520, 27720, 360360, 144144, 2450448, 232792560, 232792560, 5354228880, 26771144400, 11473347600, 332727080400, 20629078984800, 20629078984800, 144403552893600, 5342931457063200, 5342931457063200

Offset: 1

Author

Benoit Cloitre, Apr 12 2003

Keywords

• frac
• nonn
• easy

Examples

			1/2, 7/12, 37/60, 533/840, 1627/2520, 18107/27720, 237371/360360, ...
		

Links

• T. D. Noe, Table of n, a(n) for n=1..100

Crossrefs

Cf. A058312, A082687 (numerators).

Programs

Mathematica

Table[HarmonicNumber[2 n] - HarmonicNumber[n], {n, 20}] // Denominator (* Eric W. Weisstein, Dec 14 2017 *)

PARI

a(n) = denominator(sum(k=1, n, 1/(n+k))); \\ Michel Marcus, Dec 14 2017

Formula

limit n ->infinity Sum_{k=1..n} 1/(n+k) = log(2).

Denominator of Psi(2*n+1)-Psi(n+1). - Vladeta Jovovic, Aug 24 2003