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A273843 Numbers that are the average of 3 nonzero squares and the average of 2 positive cubes. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 9 13:42 EDT 2021. Contains 343742 sequences. (Running on oeis4.)