A273843 Numbers that are the average of 3 nonzero squares and the average of 2 positive cubes.

1, 8, 14, 27, 36, 63, 64, 76, 112, 140, 172, 185, 216, 234, 260, 288, 343, 364, 378, 427, 504, 512, 536, 608, 666, 679, 728, 729, 868, 896, 972, 1000, 1030, 1099, 1112, 1120, 1161, 1270, 1331, 1376, 1404, 1463, 1480, 1628, 1688, 1728, 1750, 1764, 1859, 2052, 2080, 2156

Offset

1,2

Comments

Values of (x^3 + y^3)/2 such that (x^3 + y^3)/2 = (a^2 + b^2 + c^2)/3 where x, y, a, b, c > 0, is soluble.

Links

Table of n, a(n) for n=1..52.

Example

14 is a term because 14 = (1^3 + 3^3)/2 = (1^2 + 4^2 + 5^2)/3.

Mathematica

repQ[n_, k_, e_] := {} != Quiet@ IntegerPartitions[n, {k}, Range[n^ (1/e) ]^e, 1]; Select[Range@ 2156, repQ[2*#, 2, 3] && repQ[3*#, 3, 2] &] (* Giovanni Resta, Jun 03 2016 *)

Prog

(PARI) isA000408(n) = my(a, b) ; a=1 ; while(a^2+1<n, b=1 ; while(b<=a && a^2+b^2<n, if(issquare(n-a^2-b^2), return(1) ) ; b++ ; ) ; a++ ; ) ; return(0);
isA003325(n) = for(k=1, sqrtnint(n\2, 3), ispower(n-k^3, 3) && return(1));
lista(nn) = for(n=1, nn, if(isA003325(2*n) && isA000408(3*n), print1(n, ", ")));

Crossrefs

Cf. A000408, A003325, A267702.

Sequence in context: A187062 A153340 A144842 * A227867 A254034 A225606

Adjacent sequences: A273840 A273841 A273842 * A273844 A273845 A273846

Keyword

nonn,easy

Author

Altug Alkan, Jun 01 2016

Status

approved