A273554 Numbers n such that n is the sum of two nonzero squares while n^2 is the sum of two positive cubes.

32, 98, 500, 648, 1225, 1261, 2048, 2888, 4000, 4225, 6272, 6292, 6877, 8281, 8424, 8788, 9800, 10088, 10125, 12250, 14792, 19652, 23328, 27378, 32000, 32193, 33124, 33489, 33800, 35113, 37544, 39546, 41472, 47961, 50336, 50813, 55016, 62500, 66248, 67392, 70304, 71442

Offset

1,1

Comments

In other words, values of a^2 + b^2 such that (a^2 + b^2)^2 is of the form x^3 + y^3 where a, b, x, y > 0.

Links

Table of n, a(n) for n=1..42.

Example

1261 is a term because 1261 = 6^2 + 35^2 and 1261^2 = 57^3 + 112^3.

Mathematica

nR[n_] := (SquaresR[2, n] + Plus @@ Pick[{-4, 4}, IntegerQ /@ Sqrt[{n, n/2}]])/8; nC[n_] := Length@ IntegerPartitions[n, {2}, Range[n^(1/3)]^3]; Select[ Range[10^4], nR[#] > 0 && nC[#^2] > 0 &] (* Giovanni Resta, May 25 2016 *)

Prog

(PARI) isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
isA000404(n) = for( i=1, #n=factor(n)~%4, n[1, i]==3 && n[2, i]%2 && return); n && ( vecmin(n[1, ])==1 || (n[1, 1]==2 && n[2, 1]%2));
lista(nn) = for(n=1, nn, if(isA000404(n) && isA003325(n^2), print1(n, ", ")));

Crossrefs

Cf. A000404, A003325, A050801.

Sequence in context: A190176 A198070 A197904 * A218901 A192293 A188862

Adjacent sequences: A273551 A273552 A273553 * A273555 A273556 A273557

Keyword

nonn,easy

Author

Altug Alkan, May 25 2016

Status

approved