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A267702 Numbers that are the sum of 3 nonzero squares (A000408) and the sum of 2 positive cubes (A003325). 4
9, 35, 54, 65, 72, 91, 126, 133, 152, 189, 217, 224, 243, 250, 280, 341, 344, 370, 432, 468, 513, 539, 576, 637, 686, 728, 730, 737, 756, 793, 854, 945, 1001, 1027, 1064, 1072, 1125, 1216, 1241, 1332, 1339, 1358, 1395, 1456, 1458, 1512, 1547, 1674, 1729, 1736, 1755, 1843, 1853 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Intersection of A000408 and A003325.

Sequence focuses on the solutions of equation x^3 + y^3 = a^2 + b^2 + c^2 where x, y, a, b, c > 0.

LINKS

Robert Israel, Table of n, a(n) for n = 1..3649

EXAMPLE

9 is a term because 9 = 1^3 + 2^3 = 1^2 + 2^2 + 2^2.

35 is a term because 35 = 2^3 + 3^3 = 1^2 + 3^2 + 5^2.

54 is a term because 54 = 3^3 + 3^3 = 3^2 + 3^2 + 6^2.

MAPLE

N:= 1000: # to get all terms <= N

S3:= {seq(seq(seq(a^2+b^2+c^2, c = b .. floor(sqrt(N-a^2-b^2))),

b=a .. floor(sqrt((N-a^2)/2))), a = 1 .. floor(sqrt(N/3)))}:

C2:= {seq(seq(a^3+b^3, b = a .. floor((N-a^3)^(1/3))), a = 1 .. floor((N/2)^(1/3)))}:

sort(convert(S3 intersect C2, list)); # Robert Israel, Jan 25 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); }

T=thueinit('z^3+1);

isA003325(n)=#select(v->min(v[1], v[2])>0, thue(T, n))>0;

for(n=3, 1e4, if(isA000408(n) && isA003325(n), print1(n, ", ")));

CROSSREFS

Cf. A000408, A003325.

Sequence in context: A003865 A265377 A187554 * A085366 A304913 A173245

Adjacent sequences:  A267699 A267700 A267701 * A267703 A267704 A267705

KEYWORD

nonn

AUTHOR

Altug Alkan, Jan 23 2016

STATUS

approved

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Last modified July 12 05:35 EDT 2020. Contains 335658 sequences. (Running on oeis4.)