A224484 Numbers which are the sum of two positive cubes and divisible by 3.

9, 54, 72, 126, 189, 243, 351, 432, 468, 513, 576, 756, 855, 945, 1008, 1125, 1332, 1395, 1458, 1512, 1674, 1755, 1944, 2205, 2322, 2331, 2457, 2709, 2745, 2808, 3087, 3402, 3456, 3528, 3591, 3744, 4104, 4221, 4608, 4914, 4941

Offset

1,1

Comments

If 12*h-27 is a square then some values of 3*h are in this sequence. It is easy to verify that h is of the form 3*m^2-3*m+3, and therefore 9*(m^2-m+1) = (2-m)^3+(m+1)^3.

All entries are multiples of 9. [Proof: the cubes mod 3 are A010872. So the two cubes are either of the form (3i)^3 and (3j)^3 or (3i+1)^3 and (3j+2)^3. The same 3-periodic pattern is seen in the cubes modulo 9, A167176.] - R. J. Mathar, Aug 24 2016

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Mathematica

upto[n_] := Block[{t}, Union@ Reap[ Do[If[Mod[t = x^3 + y^3, 3] == 0, Sow@ t], {x, n^(1/3)}, {y, Min[x, (n - x^3)^(1/3)]}] ][[2, 1]]]; upto[5000] (* Giovanni Resta, Jun 12 2020 *)
Module[{nn=20}, Select[Union[Total/@Tuples[Range[nn]^3, 2]], Mod[#, 3]==0 && #<nn^3&]] (* Harvey P. Dale, Mar 06 2022 *)

Crossrefs

Cf. A224485 (divisible by k=5), A101421 (k=7), A101852 (k=11), A094447 (k=13), A099178 (k=17), A102619 (k=19), A101806 (k=23), A224483 (k=29), A102658 (k=31), A102618 (k=37).

Sequence in context: A052108 A209453 A259316 * A225791 A093846 A152994

Adjacent sequences: A224481 A224482 A224483 * A224485 A224486 A224487

Keyword

nonn,easy

Author

Vincenzo Librandi, May 10 2013

Status

approved