The OEIS is supported by the many generous donors to the OEIS Foundation.
%I #25 Apr 18 2016 06:46:29
%S 9,11664,36864,38134,345744,1750329,4782969,20820969,47775744,
%T 65804544,95004009,150994944,448084224,733055625,1093955625,1416167424
%N Integers n such that both n and n^3-1 are the sum of two positive cubes (see A003325).
%C 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 38134 = 2*23*829 is the first term that is nonsquare. What are the next square terms of this sequence?
%C n is a member of A007412 and n^3 is a member of A003072, obviously.
%e 9 is a term because 9 = 1^3 + 2^3 and 9^3 - 1 = 6^3 + 8^3.
%o (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
%o for(n=1, 1e7, if(isA003325(n) && isA003325(n^3-1), print1(n, ", ")));
%Y Cf. A003325, A050787, A068601.
%K nonn,more
%O 1,1
%A _Altug Alkan_, Apr 12 2016
%E a(8)-a(16) from _Chai Wah Wu_, Apr 17 2016