

A224484


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


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
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OFFSET

1,1


COMMENTS

If 12*h27 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^23*m+3, and therefore 9*(m^2m+1) = (2m)^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 3periodic 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 *)


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



