cp's OEIS Frontend

A271717 Integers k such that both k and k^3-1 are the sum of two positive cubes (see A003325).

%I A271717 #34 Jul 21 2025 11:59:37
%S A271717 9,11664,36864,38134,345744,1750329,4782969,20820969,47775744,
%T A271717 65804544,95004009,150994944,448084224,733055625,1093955625,
%U A271717 1416167424,2197265625,4318066944,5194805625,6198727824,7169347584,10771948944,13013105625,19591041024,32427005625
%N A271717 Integers k such that both k and k^3-1 are the sum of two positive cubes (see A003325).
%C A271717 Values of a^3 + b^3 such that (a^3 + b^3)^3 - 1 is of the form x^3 + y^3 where a, b, x, y > 0.
%C A271717 38134 = 2*23*829 is the first term that is nonsquare. What are the next square terms of this sequence?
%C A271717 n is a member of A007412 and n^3 is a member of A003072, obviously.
%H A271717 Chai Wah Wu, <a href="/A271717/b271717.txt">Table of n, a(n) for n = 1..33</a>
%e A271717 9 is a term because 9 = 1^3 + 2^3 and 9^3 - 1 = 6^3 + 8^3.
%o A271717 (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
%o A271717 for(n=1, 1e7, if(isA003325(n) && isA003325(n^3-1), print1(n, ", ")));
%Y A271717 Cf. A003325, A050787, A068601.
%K A271717 nonn
%O A271717 1,1
%A A271717 _Altug Alkan_, Apr 12 2016
%E A271717 a(8)-a(16) from _Chai Wah Wu_, Apr 17 2016
%E A271717 a(17)-a(25) from _Chai Wah Wu_, Jul 21 2025