Harmonic-Number-Related Divisibility

Leroy Quet qq-quet at mindspring.com
Sun Mar 7 21:18:43 CET 2004

>> You program is false because H(n)=sum(k=1,n,1/k)  and not
>> (H(n)=sum(k=1,n,1/n))
>> > ? forprime(p=3,1000,print1(2*numerator(H(p-3))-3*denominator(H(p-3))","))
>> -3,0,14,682,7202,1262386,2710958,65111758,42020340134,389868878206,
>> 68741604516698,2649998814294866,2699193637734026,7731398516653685174,
>Yes. I will repay that by submitting the sequence.

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,...

Leroy Quet

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