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Search: id:A061798
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| A061798 |
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Number of sums i^3 + j^3 that occur more than once for 1<=i<=j<=n. |
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1
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| 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, 8, 8, 8, 9, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 13, 13, 14, 15, 16, 16, 16, 17, 17, 19, 19, 19, 19, 20, 20, 20, 21, 23, 24, 24, 24, 25, 25, 25, 25
(list; graph; listen)
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OFFSET
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1,16
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EXAMPLE
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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.
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MATHEMATICA
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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}]
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CROSSREFS
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A000217.
Sequence in context: A072746 A105390 A013941 this_sequence A029241 A103376 A045818
Adjacent sequences: A061795 A061796 A061797 this_sequence A061799 A061800 A061801
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Jun 22 2001
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