A261205 Numbers k such that floor(k^(1/m)) divides k for all integers m >= 1.

1, 2, 3, 4, 6, 8, 12, 16, 20, 24, 30, 36, 42, 48, 64, 72, 80, 120, 210, 240, 288, 324, 420, 528, 552, 576, 600, 624, 900, 1260, 1764, 1848, 1980, 3024, 6480, 8100, 8280, 11880, 14160, 14280, 14400, 14520, 14640, 28560, 43680, 44520, 46872, 50400, 175560, 331200, 346920, 491400, 809100, 3418800, 4772040, 38937600, 203918400, 2000862360

Offset: 1

Author

Yan A. Denenberg and Max Alekseyev, Aug 11 2015

Keywords

• nonn
• nice

Comments

Is this a finite sequence?

There are no other terms below 10^23. - Giovanni Resta, Aug 13 2015

Examples

			From _Michel Marcus_, Aug 13 2015: (Start)
For k=1 to 9, we have the following floored roots:
  k=1: 1, 1, ...
  k=2: 2, 1, 1, ...
  k=3: 3, 1, 1, ...
  k=4: 4, 2, 1, 1, ...
  k=5: 5, 2, 1, 1, ...
  k=6: 6, 2, 1, 1, ...
  k=7: 7, 2, 1, 1, ...
  k=8: 8, 2, 2, 1, 1, ...
  k=9: 9, 3, 2, 1, 1, ...
where one can see that 5, 7 and 9 are not terms. (End)
		

Crossrefs

Cf. A261206, A261341, A261342.

Subsequence of A006446.

Programs

Mathematica

fQ[n_] := Block[{d, k = 2, lst = {}}, While[d = Floor[n^(1/k)]; d > 1, AppendTo[lst, d]; k++]; Union[ IntegerQ@# & /@ (n/Union[lst])] == {True}]; k = 4; lst = {1, 2, 3}; While[k < 10^6, If[fQ@ k, AppendTo[lst, k]; Print@ k]; k++]; lst (* Robert G. Wilson v, Aug 15 2015 *)

PARI

is(n) = my(k,t); k=2; while( (t=sqrtnint(n, k)) > 1, if(n%t, return(0)); k++); 1
n=1; while(n<10^5,if(is(n),print1(n,", "));n++) /* Able to generate terms < 10^5 */ \\ Derek Orr, Aug 12 2015