

A191345


Numbers n with property that n and 2n are sums of two distinct positive cubes.


5



728, 756, 2457, 5824, 6048, 9288, 14364, 15561, 19656, 19684, 20412, 25327, 25389, 39816, 46592, 48384, 66339, 70336, 74304, 76167, 76895, 82251, 91000, 94500, 114912, 119574, 124488, 150444, 152208, 157248, 157472, 163296, 202616, 203112, 240002, 248976
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OFFSET

1,1


COMMENTS

Both n and 2n may be represented as a sum of two distinct positive cubes in at least one way, e.g., 19656=18^3+24^3, 2*19656=39312=2^3+34^3=15^3+33^3.
Which means, both n and 2n are terms in A024670 (numbers that are sums of 2 distinct positive cubes). E.g., n=728=A024670(27) and 2n=1456=A024670(48).
6742008 is the first n such that n and 2*n are both taxicab numbers (A001235). The next one is 53936064. In this sequence, there are infinitely many members such that n and 2*n are both taxicab numbers.  Altug Alkan, May 10 2016


LINKS



MATHEMATICA

tdpcQ[n_]:=Module[{pr1=PowersRepresentations[n, 2, 3], pr2= PowersRepresentations[ 2n, 2, 3]}, Length[pr1]>0&& Length[pr2]>0 && !MemberQ[Flatten[pr1], 0] &&!MemberQ[Flatten[pr2], 0]]; Select[Range[ 250000], tdpcQ] (* Harvey P. Dale, Jul 11 2014 *)


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



