A205788 Least positive integer j such that n divides k^3-j^3, where k, as in A205787, is the least number for which there is such a j.

1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 5, 1, 3, 2, 1, 1, 1, 4, 1, 1, 4, 2, 3, 4, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 3, 5, 1, 2, 1, 3, 1, 2, 1, 1, 1, 2, 4, 1, 1, 4, 9, 1, 2, 2, 1, 1, 1, 2, 1, 6, 5, 4, 4, 3, 3, 2, 3, 1, 1, 2, 1, 9, 1, 2, 1, 1, 5, 2, 4, 1, 4, 4, 3, 3, 1

Offset

1,4

Comments

For a guide to related sequences, see A204892.

Links

Table of n, a(n) for n=1..99.

Example

1 divides 2^3-1^3 -> k=2, j=1
2 divides 3^3-1^3 -> k=3, j=1
3 divides 4^3-1^3 -> k=4, j=3
4 divides 4^3-2^3 -> k=4, j=2
5 divides 6^3-1^3 -> k=6, j=1

Mathematica

s = Table[n^3, {n, 1, 120}] ;
lk = Table[
  NestWhile[# + 1 &, 1,
   Min[Table[Mod[s[[#]] - s[[j]], z], {j, 1, # - 1}]] =!= 0 &], {z, 1,
    Length[s]}]
Table[NestWhile[# + 1 &, 1,
  Mod[s[[lk[[j]]]] - s[[#]], j] =!= 0 &], {j, 1, Length[lk]}]
(* Peter J. C. Moses, Jan 27 2012 *)

Crossrefs

Cf. A204892.

Sequence in context: A050330 A339890 A351408 * A214054 A330739 A076398

Adjacent sequences: A205785 A205786 A205787 * A205789 A205790 A205791

Keyword

nonn

Author

Clark Kimberling, Feb 01 2012

Status

approved