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

1,2

Comments

There are no other terms below 10^16.

Is this a finite sequence?

Links

Table of n, a(n) for n=1..22.

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 *)

Prog

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

Crossrefs

Cf. A261205, A261206

Subsequence of A006446 and A261342.

Sequence in context: A332345 A095912 A143474 * A220423 A335068 A372092

Adjacent sequences: A261338 A261339 A261340 * A261342 A261343 A261344

Keyword

nonn,more

Author

Max Alekseyev, Aug 15 2015

Status

approved