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%I #22 Sep 09 2022 16:02:38
%S 1,1,13,29,731,4357,136141,1497401,52856987,698076077,49526267143,
%T 574253997269,72925181864501,1123720869207397,143426539122302791,
%U 2236629947933814637,422054527184135696827,8864360144543549996813
%N Absolute value of the numerator of Sum_{i=1..n} (-1)^i * i/prime(i).
%H G. C. Greubel, <a href="/A120273/b120273.txt">Table of n, a(n) for n = 1..300</a>
%F a(n) = abs(numerator(Sum_{i=1..n} (-1)^i * i/prime(i))).
%F a(n) = abs(Sum_{i=1..n} ((i(-1)^i * (Product_{k=1..n} prime(k)))/prime(i))). - _Petr Platais_, Aug 14 2022
%t Abs[Numerator[Table[Sum[(-1)^i*i/Prime[i],{i,1,n}],{n,1,20}]]]
%t Abs[Table[Sum[(m*(-1)^m*Product[Prime[n], {n, 1, k}])/Prime[m], {m, 1, k}], {k, 1, 20}]] (* _Petr Platais_, Aug 11 2022 *)
%o (PARI) for(n=1,20, print1(numerator(abs(sum(k=1,n, (-1)^k*k/prime(k)))), ", ")) \\ _G. C. Greubel_, Aug 23 2018
%o (Magma) [Numerator(Abs((&+[(-1)^k*k/NthPrime(k): k in [0..n]]))): n in [1..20]]; // _G. C. Greubel_, Aug 23 2018
%K frac,nonn
%O 1,3
%A _Alexander Adamchuk_, Jul 01 2006