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A206803 Sum_{0-P(j), where P(j)=A065091(j) is the j-th odd prime.

%I A206803 #14 Apr 19 2015 00:16:47
%S A206803 2,8,26,52,98,156,242,376,528,740,996,1276,1608,2024,2530,3068,3708,
%T A206803 4420,5170,6040,6994,8080,9350,10716,12132,13652,15226,16912,19004,
%U A206803 21216,23614,26076,28868,31728,34798,38084,41518,45180,49076
%N A206803 Sum_{0<j<k<=n} P(k)-P(j), where P(j)=A065091(j) is the j-th odd prime.
%C A206803 Partial sums of A185382.
%H A206803 Danny Rorabaugh, <a href="/A206803/b206803.txt">Table of n, a(n) for n = 2..10000</a>
%t A206803 s[k_] := Prime[k + 1]; t[1] = 0;
%t A206803 p[n_] := Sum[s[k], {k, 1, n}];
%t A206803 c[n_] := n*s[n] - p[n]
%t A206803 t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
%t A206803 Table[c[n], {n, 2, 100}]  (* A185382 *)
%t A206803 %/2  (* A206802 *)
%t A206803 Flatten[Table[t[n], {n, 2, 40}]]  (*  A206803 *)
%t A206803 %/2  (* A206804 *)
%o A206803 (Sage) [sum([sum([nth_prime(k+1)-nth_prime(j+1) for j in range(1,k)]) for k in range(2,n+1)]) for n in range(2,41)] # _Danny Rorabaugh_, Apr 18 2015
%Y A206803 Cf. A065091, A185382, A206804, A206817.
%K A206803 nonn
%O A206803 2,1
%A A206803 _Clark Kimberling_, Feb 13 2012