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A120308 Numerator((p-1)*H(p-1))/p^2 for p = prime(n) > 3, where H(k) is k-th harmonic number A001008(k)/A002805(k).

%I A120308 #23 Sep 08 2022 08:45:25
%S A120308 1,3,61,509,8431,118623,36093,375035183,9682292227,40030624861,
%T A120308 1236275063173,46600968591317,2690511212793403,5006621632408586951,
%U A120308 73077117446662772669,4062642402613316532391,139715526178793824689891
%N A120308 Numerator((p-1)*H(p-1))/p^2 for p = prime(n) > 3, where H(k) is k-th harmonic number A001008(k)/A002805(k).
%H A120308 G. C. Greubel, <a href="/A120308/b120308.txt">Table of n, a(n) for n = 3..344</a>
%F A120308 a(n) = numerator((prime(n)-1)*(Sum_{k=1..prime(n)-1} 1/k))/prime(n)^2 for n > 2.
%F A120308 a(n) = A096617(p-1)/p^2 for p = prime(n) > 3.
%p A120308 N:= 50: # to get the first N terms
%p A120308 Primes:= select(isprime,[seq(2*i+1,i=2..(ithprime(N+2)-1)/2)]):
%p A120308 H:= ListTools[PartialSums]([seq(1/i,i=1..Primes[-1]-1)]):
%p A120308 seq(numer((p-1)*H[p-1])/p^2, p=Primes); # _Robert Israel_, Sep 09 2014
%t A120308 Numerator[Table[(Prime[n]-1)*(Sum[(1/k), {k, 1, Prime[n]-1}]),{n,3,20}]]/Table[Prime[n]^2,{n,3,20}]
%t A120308 Table[((p-1)HarmonicNumber[p-1])/p^2,{p,Prime[Range[2,20]]}]//Numerator (* _Harvey P. Dale_, May 19 2021 *)
%o A120308 (PARI) {a(n) = numerator((prime(n)-1)*sum(k=1,prime(n)-1, 1/k)/prime(n)^2)};
%o A120308 for(n=3,25, print1(a(n), ", ")) \\ _G. C. Greubel_, Sep 02 2018
%o A120308 (Magma) [Numerator((NthPrime(n)-1)*HarmonicNumber(NthPrime(n)-1)/NthPrime(n)^2): n in [3..25]]; // _G. C. Greubel_, Sep 02 2018
%Y A120308 Cf. A096617, A001008, A002805.
%K A120308 frac,nonn
%O A120308 3,2
%A A120308 _Alexander Adamchuk_, Jul 16 2006