A265377 Sums of two or more consecutive positive cubes.

9, 35, 36, 91, 99, 100, 189, 216, 224, 225, 341, 405, 432, 440, 441, 559, 684, 748, 775, 783, 784, 855, 1071, 1196, 1241, 1260, 1287, 1295, 1296, 1584, 1729, 1800, 1925, 1989, 2016, 2024, 2025, 2241, 2331, 2584, 2800, 2925, 2989, 3016, 3024, 3025, 3059, 3060

Offset: 1

Author

Robert Israel, Dec 07 2015

Keywords

• nonn

Comments

All numbers of the form A000537(b) - A000537(a) for 0 <= a <= b-2.

A217843 minus (A000578 minus A131643).

n is in the sequence iff n = s*t where (s+t)/2 = A000217(u) and (s-t)/2 = A000217(v) with u-v >= 2.

If a(k(n)) = A000537(n+1), k(n) >= A000217(n) for n > 0. - Altug Alkan, Dec 07 2015

See A062682 for sums of two or more consecutive positive cubes in more than one way. - Reinhard Zumkeller, Dec 16 2015

Examples

			a(1) = 1^3 + 2^3 = 9.
a(2) = 2^3 + 3^3 = 35.
a(3) = 1^3 + 2^3 + 3^3 = 36.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Subset of A217843.

Cf. A000217, A000537, A000578, A131643.

Cf. A062682 (subsequence).

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert, Set)
a265377 n = a265377_list !! (n-1)
a265377_list = f (singleton (1 + 2^3, (1, 2))) (-1) where
   f s z = if y /= z then y : f s'' y else f s'' y
              where s'' = (insert (y', (i, j')) $
                           insert (y' - i ^ 3 , (i + 1, j')) s')
                    y' = y + j' ^ 3; j' = j + 1
                    ((y, (i, j)), s') = deleteFindMin s
-- Reinhard Zumkeller, Dec 17 2015

Maple

amin:= proc(b,N) local r;
  r:= b^2*(b+1)^2 - 4*N; if r > 0 then iroot(r,4) else 1 fi
end proc:
A265377:= proc(N) # to get all terms <= N
  local  a,b;
  sort(convert(select(`<=`,{seq(seq(b^2*(b+1)^2/4 - a^2*(a-1)^2/4,
       a = amin(b,N) .. b-1), b=2..1+iroot(floor(N/2),3))},N),list))
end proc:
A265377(10000);

Mathematica

With[{nn=12},Select[Sort[Flatten[Table[Total/@Partition[Range[nn]^3,n,1],{n,2,nn}]]],#<=((nn(nn+1))/2)^3&]] (* Harvey P. Dale, Dec 25 2015 *)