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A206802 a(n) = (1/2)*A185382(n).

%I A206802 #21 Sep 14 2016 17:32:06
%S A206802 1,3,9,13,23,29,43,67,76,106,128,140,166,208,253,269,320,356,375,435,
%T A206802 477,543,635,683,708,760,787,843,1046,1106,1199,1231,1396,1430,1535,
%U A206802 1643,1717,1831,1948,1988,2193,2235,2321,2365,2635,2911,3005
%N A206802 a(n) = (1/2)*A185382(n).
%C A206802 See A185382.
%t A206802 s[k_] := Prime[k + 1]; t[1] = 0;
%t A206802 p[n_] := Sum[s[k], {k, 1, n}];
%t A206802 c[n_] := n*s[n] - p[n]
%t A206802 t[n_] := t[n - 1] + (n - 1) s[n] - p[n - 1]
%t A206802 Table[c[n], {n, 2, 100}]  (* A185382 *)
%t A206802 %/2  (* A206802 *)
%t A206802 Flatten[Table[t[n], {n, 2, 40}]]  (*  A206803 *)
%t A206802 %/2  (* A206804 *)
%t A206802 Table[Sum[Prime[n + 1] - Prime[j + 1], {j, n - 1}]/2, {n, 2, 48}] (* _Michael De Vlieger_, Sep 13 2016 *)
%Y A206802 Cf. A185382.
%K A206802 nonn
%O A206802 2,2
%A A206802 _Clark Kimberling_, Feb 13 2012