A061798 Number of sums i^3 + j^3 that occur more than once for 1<=i<=j<=n.

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

Offset

1,16

Links

Seiichi Manyama, Table of n, a(n) for n = 1..1000

Example

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.

Mathematica

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}]

Crossrefs

Cf. A000217, A061791.

Sequence in context: A105390 A347941 A013941 * A345206 A318585 A029241

Adjacent sequences: A061795 A061796 A061797 * A061799 A061800 A061801

Keyword

nonn

Author

Labos Elemer, Jun 22 2001

Status

approved