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%I #7 Feb 19 2022 07:07:03
%S 2,3,4,5,6,7,12,35,43,73,77,93,98,151,166,224,255,372,596,602,813,934,
%T 1139,1373,1397,1411,1530,1892,1954,2236,2275,2930,3209,3257,3420,
%U 4493,5002,5553,6173,6599,7615,8601,8785,10895,10923,11161,12118,14451,15741
%N Numbers k such that the numerator of Sum_{j=1..k} k^2/(2*j*(j+k)) is prime.
%C Posted in response to a question from Dirk Boland.
%e a(7) = 12 is a term because Sum_{j=1..k} k^2/(2*j*(j+k)) = 13013256143/892371480, for k=12, 13013256143 is prime and this is the 7th such sum with a prime numerator.
%t q[n_] := PrimeQ[Numerator[Sum[n^2/(2*j*(j + n)), {j, 1, n}]]]; Select[Range[1000], q] (* _Amiram Eldar_, Feb 19 2022 *)
%o (PARI) {ls=[];for(k=1,250, if(ispseudoprime(numerator(sum(j=1,k,k^2/(2*j*(j+k))))), ls=concat(ls,k)));print(ls)}
%K nonn
%O 1,1
%A _David Broadhurst_, Dec 05 2006
%E a(30)-a(49) from _Amiram Eldar_, Feb 19 2022