A061791 Number of distinct sums i^3 + j^3 for 1<=i<=j<=n.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 77, 90, 104, 119, 134, 151, 169, 188, 208, 229, 251, 274, 297, 322, 348, 374, 402, 431, 461, 492, 523, 556, 588, 623, 658, 695, 733, 771, 810, 851, 893, 936, 980, 1025, 1071, 1118, 1164, 1213, 1263, 1313, 1365, 1417

Offset: 1

Author

Labos Elemer, Jun 22 2001

Keywords

• nonn

Examples

			If the {s+t} sums are generated by addition 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.
		

Links

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

Crossrefs

Cf. A000217, A061798.

Programs

Mathematica

f[x_] := x^3 t=Table[Length[Union[Flatten[Table[f[u]+f[w], {w, 1, m}, {u, 1, m}]]]], {m, 1, 75}]

Ruby

def A(n)
  h = {}
  (1..n).each{|i|
    (i..n).each{|j|
      k = i * i * i + j * j * j
      if h.has_key?(k)
        h[k] += 1
      else
        h[k] = 1
      end
    }
  }
  h.size
end
def A061791(n)
  (1..n).map{|i| A(i)}
end
p A061791(60) # Seiichi Manyama, May 14 2024