A251781 Numbers whose square is the sum of two distinct positive cubes.

3, 24, 81, 98, 168, 192, 228, 312, 375, 525, 588, 648, 671, 784, 847, 1014, 1029, 1183, 1225, 1261, 1323, 1344, 1536, 1824, 2187, 2496, 2646, 2888, 3000, 3993, 4200, 4225, 4536, 4563, 4644, 4704, 5184, 5368, 6156, 6272, 6292, 6371, 6591, 6696, 6776, 6877, 8112

Offset

1,1

Comments

This list contains A117642 (if n=3*k^3, then n^2 = 9*k^6 = 8*k^6 + k^6 = (2*k^2)^3 + (k^2)^3). (Old comment rewritten as suggested by Michel Marcus, Dec 10 2014.)

Subsequence of A050801 and A217248. - Wolfdieter Lang, Jan 04 2015

Links

Daniel Arribas, Table of n, a(n) for n = 1..575

Example

3^2 = 1^3 + 2^3; 24^2 = 4^3 + 8^3.

Prog

(Sage)
L = []
for k in range(1, 10^3):
    for l in range(k + 1, 10^3):
        if is_square(k**3+l**3):
            L.append(sqrt(k**3+l**3))
(Python)
def aupto(limit):
  c = [i**3 for i in range(1, int(limit**(2/3))+2) if i**3 <= limit**2]
  cc = [c1 + c2 for i, c1 in enumerate(c) for c2 in c[i+1:]]
  return sorted([i for i in range(1, limit+1) if i*i in cc])
print(aupto(8122)) # Michael S. Branicky, Mar 24 2021

Crossrefs

Cf. A024670, A117642, A050801, A217248, A099426 (coprime positive cubes).

Sequence in context: A092468 A347108 A027158 * A117642 A220834 A276243

Adjacent sequences: A251778 A251779 A251780 * A251782 A251783 A251784

Keyword

nonn

Author

Daniel Arribas, Dec 08 2014

Status

approved