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

%I A251781 #34 Mar 24 2021 15:52:29
%S A251781 3,24,81,98,168,192,228,312,375,525,588,648,671,784,847,1014,1029,
%T A251781 1183,1225,1261,1323,1344,1536,1824,2187,2496,2646,2888,3000,3993,
%U A251781 4200,4225,4536,4563,4644,4704,5184,5368,6156,6272,6292,6371,6591,6696,6776,6877,8112
%N A251781 Numbers whose square is the sum of two distinct positive cubes.
%C A251781 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.)
%C A251781 Subsequence of A050801 and A217248. - _Wolfdieter Lang_, Jan 04 2015
%H A251781 Daniel Arribas, <a href="/A251781/b251781.txt">Table of n, a(n) for n = 1..575</a>
%e A251781 3^2 = 1^3 + 2^3; 24^2 = 4^3 + 8^3.
%o A251781 (Sage)
%o A251781 L = []
%o A251781 for k in range(1,10^3):
%o A251781     for l in range(k + 1,10^3):
%o A251781         if is_square(k**3+l**3):
%o A251781             L.append(sqrt(k**3+l**3))
%o A251781 (Python)
%o A251781 def aupto(limit):
%o A251781   c = [i**3 for i in range(1, int(limit**(2/3))+2) if i**3 <= limit**2]
%o A251781   cc = [c1 + c2 for i, c1 in enumerate(c) for c2 in c[i+1:]]
%o A251781   return sorted([i for i in range(1, limit+1) if i*i in cc])
%o A251781 print(aupto(8122)) # _Michael S. Branicky_, Mar 24 2021
%Y A251781 Cf. A024670, A117642, A050801, A217248, A099426 (coprime positive cubes).
%K A251781 nonn
%O A251781 1,1
%A A251781 _Daniel Arribas_, Dec 08 2014