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A274128 Numbers n such that n and n^2 are both a sum of two positive cubes. 1
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 (list; graph; refs; listen; history; text; internal format)
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: A250515 A031667 A196200 * A144306 A234033 A253940

Adjacent sequences:  A274125 A274126 A274127 * A274129 A274130 A274131

KEYWORD

nonn

AUTHOR

Altug Alkan, Jun 10 2016

STATUS

approved

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Last modified February 19 19:06 EST 2020. Contains 332047 sequences. (Running on oeis4.)