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A273554 Numbers n such that n is the sum of two nonzero squares while n^2 is the sum of two positive cubes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 8 11:31 EDT 2020. Contains 336298 sequences. (Running on oeis4.)