A191383 Integers n such that each of n, 2n and 3n is a sum of 2 distinct positive cubes.

2457, 15561, 19656, 25389, 39816, 66339, 124488, 157248, 203112, 248976, 307125, 318528, 420147, 530712, 685503, 842751, 995904, 1075032, 1257984, 1624896, 1791153, 1945125, 1991808, 2457000, 2548224, 3173625, 3270267

Offset: 1

Author

Zak Seidov, Jun 01 2011

Keywords

• nonn

Examples

			2457 is in the sequence because 2457 = 9^3+12^3, 2*2457 = 4914 = 1^3+17^3, 3*2457 = 7371 = 8^3+19^3 have at least one representation as a sum of two distinct positive cubes.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2605

Crossrefs

Cf. A024670, A191345, A191352.

Programs

Maple

isA000578 := proc(n) option remember; local f; for f in ifactors(n)[2] do if op(2,f) mod 3 <> 0 then return false; end if; end do: true ; end proc:
isA024670 := proc(n) option remember ; local k,kc,k3 ; for k from 1 do k3 := k^3 ; kc := n-k^3 ; if kc <= k3 then return false; elif isA000578(kc) then return true; end if; end do: end proc:
isA191383 := proc(n) isA024670(n) and isA024670(2*n) and isA024670(3*n) ; end proc:
for n from 1 do if isA191383(n) then printf("%d,\n",n); end if; end do: # R. J. Mathar, Jun 03 2011

Formula

{n: n in A024670 and 2n in A024670 and 3n in A024670}.