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%I #6 Oct 15 2013 22:31:02
%S 1,3,3,5,5,7,7,7,7,7,7,10,10,10,10,11,11,11,11,11,11,11,11,14,14,14,
%T 14,14,14,14,14,14,14,14,14,17,17,17,17,17,17,17,17,17,17,17,17,19,19,
%U 19,19,19,19,19,19,19,19,19,19,22,22,22,22,22,22,22,22,22,22,22,22,22,22
%N Number of distinct sums d(i) + d(j) for 1<=i<=j<=n, d(k) = A000005(k) = number of divisors function.
%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 tau-values gives results falling between these two extremes. E.g. n=10, A000005:{1,2,2,3,2,4,2,4,3,4...}; possible values of sum of 2:{2,3,4,5,6,7,8}, thus a(10)=7.
%t f[x_] := DivisorSigma[0, x] t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]
%Y A000217, A000005.
%K nonn
%O 1,2
%A _Labos Elemer_, Jun 22 2001
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