Harmonic-Number-Related Divisibility

[bouyao]

> That first term is indeed -3, not 0 as I had, since we want the numerator
> and denominator to be coprime, and 1 is the only positive integer coprime
> to 0.
>
> But this sequence is interesting mainly because the k_th term is
> divisible by the k_th odd prime.
>
> Could someone please (also) submit, if it is not already in the EIS, the
> above sequence divided by the appropriate odd primes?
>
> -1, 0, 2, 62, 554, 74258,...
>
> thanks,
> Leroy Quet
>

Dear, Leroy,

the sequence is :
-1,0,2,62,554,74258,142682,2830946,1448977246,12576415426,1857881203154,
64634117421826,62771945063582,164497840779865642,
350742295126606034006,5774653629556529218142,5647762835059481932498,
12720214895833193424471634,273052345163461362610194682,
803653788192693403642362802,11829925877566918701087121863254,
82072922368546053187154299642718,
58361337009078105995966076213150542,
53734412249161723800809907275773898026,

Thanks

M.Bouayoun