Search: id:A061798
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%I A061798
%S A061798 0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,2,2,2,2,2,2,2,2,3,3,3,4,4,4,4,4,5,5,7,7,
%T A061798 8,8,8,9,10,10,10,10,10,10,10,10,12,12,12,13,13,14,15,16,16,16,17,17,
%U A061798 19,19,19,19,20,20,20,21,23,24,24,24,25,25,25,25
%N A061798 Number of sums i^3 + j^3 that occur more than once for 1<=i<=j<=n.
%e A061798 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 cubes gives results 
               falling between these two extremes. E.g. S={1,8,27,...,2744,3375} 
               provides 119 different sums of two, not necessarily different cubes:{2,
               9,....,6750}. Only a single sum occurs more than once: 1729(Ramanujan): 
               1729=1+1728=729+1000. Therefore a(15)=C[15,2]+15-119=120-119=1.
%t A061798 f[x_] := x^3 t0=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, 
               {u, 1, m}]]]], {m, 1, 75}] t1=Table[(w*(w+1)/2)-Part[t0, w], {w, 
               1, 75}]
%Y A061798 A000217.
%Y A061798 Sequence in context: A072746 A105390 A013941 this_sequence A029241 A103376 
               A045818
%Y A061798 Adjacent sequences: A061795 A061796 A061797 this_sequence A061799 A061800 
               A061801
%K A061798 nonn
%O A061798 1,16
%A A061798 Labos E. (labos(AT)ana.sote.hu), Jun 22 2001

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