A261341 Numbers n such that round(n^(1/k)) divides n for all integers k>=1.

1, 2, 4, 6, 12, 30, 36, 42, 72, 240, 420, 600, 900, 1560, 1764, 3600, 6084, 8100, 46440, 1742400, 4062240, 35814240

Offset: 1

Author

Max Alekseyev, Aug 15 2015

Keywords

• nonn
• more

Comments

There are no other terms below 10^16.

Is this a finite sequence?

Crossrefs

Cf. A261205, A261206

Subsequence of A006446 and A261342.

Programs

Mathematica

isA[n_] :=
Block[{t},
  For[k = 2, (t = Floor[1/2 + n^(1/k)]) >= 2, k++,
   If[Mod[n, t] != 0, Return[False]]]; Return[True]]
Select[Range[1, 100000], isA[#] &] (* Julien Kluge, Apr 04 2016 *)

PARI

{ isA261341(n) = my(k,t); k=2; until(t<=2, t=round(sqrtn(n,k)); if(n%t,return(0)); k++); 1; }