A274128 Numbers n such that n and n^2 are both a sum of two positive cubes.

39312, 251370, 314496, 432523, 948051, 1061424, 1536416, 2010960, 2515968, 3009825, 3460184, 4914000, 6786990, 6822900, 7154784, 7584408, 7825545, 8491392, 11678121, 12291328, 13484016, 16087680, 20127744, 24078600, 25501762, 25597377

Offset

1,1

Comments

Numbers n such that n^k is the sum of two positive cubes for all k not divisible by 3.

The restriction on the values of k is the result of Fermat's Last Theorem.

Inspiration was Taxi-cab number 39312. It is the least number with the property that sequence focuses on.

Links

Chai Wah Wu, Table of n, a(n) for n = 1..1646

Example

251370 is a term because 251370 = 29^3 + 61^3 and 251370^2 = 2961^3 + 3339^3.

Prog

(PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(n) && isA003325(n^2), print1(n, ", ")));

Crossrefs

Cf. A003325.

Sequence in context: A031667 A196200 A378627 * A144306 A234033 A253940

Adjacent sequences: A274125 A274126 A274127 * A274129 A274130 A274131

Keyword

nonn

Author

Altug Alkan, Jun 10 2016

Status

approved