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%I #12 Feb 07 2016 10:48:30
%S 2457,15561,19656,25389,39816,66339,124488,157248,203112,248976,
%T 307125,318528,420147,530712,685503,842751,995904,1075032,1257984,
%U 1624896,1791153,1945125,1991808,2457000,2548224,3173625,3270267
%N Integers n such that each of n, 2n and 3n is a sum of 2 distinct positive cubes.
%H Chai Wah Wu, <a href="/A191383/b191383.txt">Table of n, a(n) for n = 1..2605</a>
%F {n: n in A024670 and 2n in A024670 and 3n in A024670}.
%e 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.
%p 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:
%p 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:
%p isA191383 := proc(n) isA024670(n) and isA024670(2*n) and isA024670(3*n) ; end proc:
%p for n from 1 do if isA191383(n) then printf("%d,\n",n); end if; end do: # _R. J. Mathar_, Jun 03 2011
%Y Cf. A024670, A191345, A191352.
%K nonn
%O 1,1
%A _Zak Seidov_, Jun 01 2011
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