A124432 Denominator of Sum_{k=1..n} 1/H(k), where H(k) = Sum_{j=1..k} 1/j is the k-th harmonic number.

1, 1, 3, 33, 825, 113025, 5538225, 60920475, 46360481475, 330503872435275, 20160736218551775, 1687675389591187637025, 145175524688023551724527525, 166370135063802174111446471957325, 194941377468714112878127508925972294225

Offset: 0

Author

Leroy Quet, Dec 15 2006

Keywords

• frac
• nonn

Comments

If p > 3 is prime, then p^2 divides a(p-1). - Thomas Ordowski, Mar 24 2023

Crossrefs

Cf. A096987 (numerators), A001008, A002805.

Programs

Mathematica

f[n_] := Denominator[ Sum[ 1/HarmonicNumber[j], {j, n}]]; Table[ f[n], {n, 0, 14}] (* Ray Chandler, Dec 16 2006 *)

PARI

a(n) = denominator(sum(k=1, n, 1/sum(j=1, k, 1/j))); \\ Michel Marcus, Mar 24 2023

Extensions

Extended by Ray Chandler and Robert G. Wilson v, Dec 16 2006