A205787 - OEIS

%I #10 Jul 10 2020 03:51:22

%S 2,3,4,4,6,7,2,4,4,11,12,8,3,4,16,6,18,7,3,12,4,23,24,8,10,3,6,4,30,

%T 31,5,8,34,35,9,8,4,6,5,12,42,8,6,24,16,47,48,14,5,15,52,6,54,9,56,4,

%U 7,59,60,32,5,5,4,8,14,67,7,36,70,11,72,8,8,8,20,6,15,9,7,22,12

%N Least positive integer k such that n divides k^3-j^3 for some j in [1,k-1].

%C For a guide to related sequences, see A204892.

%C 1 divides 2^3-1^3 -> k=2, j=1

%C 2 divides 3^3-1^3 -> k=3, j=1

%C 3 divides 4^3-1^3 -> k=4, j=3

%C 4 divides 4^3-2^3 -> k=4, j=2

%C 5 divides 6^3-1^3 -> k=6, j=1

%t s = Table[n^3, {n, 1, 120}] ;

%t lk = Table[

%t   NestWhile[# + 1 &, 1,

%t    Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1,

%t     Length[s]}]

%t Table[NestWhile[# + 1 &, 1,

%t   Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]

%t (* _Peter J. C. Moses_, Jan 27 2012 *)

%K nonn

%O 1,1

%A _Clark Kimberling_, Feb 01 2012