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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, 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; refs; listen; history; text; internal format)
OFFSET

1,16

LINKS

Table of n, a(n) for n=1..75.

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

A000217.

Sequence in context: A179528 A105390 A013941 * A318585 A029241 A226749

Adjacent sequences:  A061795 A061796 A061797 * A061799 A061800 A061801

KEYWORD

nonn

AUTHOR

Labos Elemer, Jun 22 2001

STATUS

approved

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Last modified October 21 12:36 EDT 2018. Contains 316419 sequences. (Running on oeis4.)