A191345 Numbers n with property that n and 2n are sums of two distinct positive cubes.

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

Offset: 1

Author

Zak Seidov, May 30 2011

Keywords

• nonn

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 taxi-cab numbers (A001235). The next one is 53936064. In this sequence, there are infinitely many members such that n and 2*n are both taxi-cab numbers. - Altug Alkan, May 10 2016

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A024670.

Programs

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 *)