%I #5 Oct 31 2013 12:25:41
%S 1,2,3,6,8,12,15,25,32,48,53,106,265,318,321,428,642,2563,5713,15019,
%T 113573,230801,306127,941071,1016963,5166859,9536294,30956561,
%U 123081011,265811669,1016775247,3050325741,4354364461,14086296281,60060345973
%N Records in A109890.
%t a[1] = 1; a[2] = 2; a[n_] := a[n] = Block[{t = Table[a[i], {i, n - 1}]}, s = Plus @@ t; d = Divisors[s]; l = Complement[d, t]; If[l != {}, k = First[l], k = s; While[Position[t, k] == {}, k += s]; k]]; b = 0; t = {}; Do[If[a[n] > b, b = a[n]; AppendTo[t, b]], {n, 2500}]; t (_Robert G. Wilson v_)
%Y Cf. A109890, A111243.
%K nonn
%O 1,2
%A _N. J. A. Sloane_, Oct 30 2005
%E More terms from _Robert G. Wilson v_, Nov 03 2005