%I #20 Jun 19 2016 21:43:43

%S 27,227,335,2387,9299,104571,113519,118499,212343,258999,328499,

%T 455600,699891,820755,971360,977051,1059239,1119723,1193631,1421367,

%U 1604084,2231999,2794067,4191431,5450948,6054611,6769607,7672391,7760639,7875035,8091615,9606203,15511268

%N Integers n such that n^3 + 1 is the average of two positive cubes.

%C Integers n such that n^3 + 1 is the average of two distinct positive cubes.

%e 27 is a term because 27^3 + 1 = (4^3 + 34^3)/2.

%o (PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));

%o lista(nn) = for(n=1, nn, if(isA003325(2*(n^3+1)), print1(n, ", ")));

%Y Cf. A001093, A003325.

%K nonn

%O 1,1

%A _Altug Alkan_, May 31 2016

%E a(9)-a(12) from _Giovanni Resta_, Jun 01 2016

%E a(13)-a(33) from _Chai Wah Wu_, Jun 19 2016