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%I #5 Oct 15 2013 22:31:02
%S 1,3,6,9,12,17,18,23,27,30,30,39,40,45,45,51,51,60,60,66,69,72,72,81,
%T 81,81,86,92,94,103,103,112,112,114,114,131,133,133,133,141,141,151,
%U 153,155,157,157,157,175,178,185,185,193,193,202,202,202,205,205,205
%N Number of distinct sums sigma(i) + sigma(j) for 1<=i<=j<=n, where sigma(k) = A000203(k).
%e If the {s+t} sums are generated by adding 2 terms of an S set consisting of n different entries, then at least 1, at most n(n+1)/2=A000217(n) distinct values can be obtained. The set of first n sigma-values gives results falling between these two extremes.
%e E.g. n=10, A000203: {1,3,4,7,6,12,8,15,13,18...}. The 55 possible sigma(i)+sigma(j) additions give 30 different results: {2,4,5,6,...,33,36}. Therefore a(10)=30.
%t f[x_] := DivisorSigma[1, x] t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]
%Y Cf. A000217, A000203.
%K nonn
%O 1,2
%A _Labos Elemer_, Jun 22 2001
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