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%I #17 Jun 18 2016 00:28:56
%S 39312,251370,314496,432523,948051,1061424,1536416,2010960,2515968,
%T 3009825,3460184,4914000,6786990,6822900,7154784,7584408,7825545,
%U 8491392,11678121,12291328,13484016,16087680,20127744,24078600,25501762,25597377
%N Numbers n such that n and n^2 are both a sum of two positive cubes.
%C Numbers n such that n^k is the sum of two positive cubes for all k not divisible by 3.
%C The restriction on the values of k is the result of Fermat's Last Theorem.
%C Inspiration was Taxi-cab number 39312. It is the least number with the property that sequence focuses on.
%H Chai Wah Wu, <a href="/A274128/b274128.txt">Table of n, a(n) for n = 1..1646</a>
%e 251370 is a term because 251370 = 29^3 + 61^3 and 251370^2 = 2961^3 + 3339^3.
%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(n) && isA003325(n^2), print1(n, ", ")));
%Y Cf. A003325.
%K nonn
%O 1,1
%A _Altug Alkan_, Jun 10 2016