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%I #24 Feb 27 2018 02:59:35
%S 1,6,17,34,57,2,121,6,23,262,321,386,55,534,617,88,3,902,61,144,77,52,
%T 9,1634,1777,1926,17,2242,2409,344,2761,198,3137,4,3537,164,535,4182,
%U 4409,112,93,5126,5377,768,413,6166,453,920,7009,7302,1043,22,8217,224,13,9186,5,34,10209,188,19,1560,11657
%N a(n) = min( x : x^3 + n^3 == 0 mod (x+n-1) ).
%F a(n) = 3*n^2 - 4*n + 2 for n=1, 2, 3, 4, 5, 7, 10, 11, 12, 14, 15, 18, 24, 25, 26, 28, 29, 31, 33, 35, 38, ...
%F That is, in those cases a(n) = A056109(n-1). It appears that the corresponding indices are given by A133431 (i.e., 1 U A002504). - _Michel Marcus_, Feb 17 2018
%t a[n_] := For[x = 1, True, x++, If[Mod[x^3 + n^3, x + n - 1] == 0, Return[x]]]; Array[a, 24] (* _Jean-François Alcover_, Feb 17 2018 *)
%o (PARI) a(n) = {my(k=1); while((k^3+n^3)%(k+n-1) != 0, k++); k; } \\ _Altug Alkan_, Feb 17 2018
%Y Cf. A066333.
%K nonn
%O 1,2
%A _Benoit Cloitre_, Jan 02 2002
%E More terms from _Altug Alkan_, Feb 17 2018
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