Harmonic-Number-Related Divisibility

[Leroy Quet]

Let H(m) be the m_th harmonic number:

H(m) = 1 + 1/2 + 1/3 + ...+ 1/m.

If we represent H(m) as a reduced fraction (and even if we do not reduce, 
for that matter...), I once proved that:

If p = odd prime, then

p divides (2*numerator(H(p-3)) -3*denominator(H(p-3))).



But I forgot now the specifics of the proof (or "proof"), which I hope is 
correct.


So, what about the sequence of

(2*numerator(H(p-3)) -3*denominator(H(p-3)))/p,

where the k_th term is for the k_th odd prime p?
(and we DO reduce)


0, 0, 2, 62,...


What can be said about this sequence, such as its factorization?

(Not in the EIS, but "2, 62" brings up a bunch of hits, which probably 
means very little.)

thanks,
Leroy
Quet