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Numbers n such that round(n^(1/k)) divides n for all integers k>=1.
3

%I #12 Sep 27 2023 12:54:43

%S 1,2,4,6,12,30,36,42,72,240,420,600,900,1560,1764,3600,6084,8100,

%T 46440,1742400,4062240,35814240

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

%C There are no other terms below 10^16.

%C Is this a finite sequence?

%t isA[n_] :=

%t Block[{t},

%t For[k = 2, (t = Floor[1/2 + n^(1/k)]) >= 2, k++,

%t If[Mod[n, t] != 0, Return[False]]]; Return[True]]

%t Select[Range[1, 100000], isA[#] &] (* _Julien Kluge_, Apr 04 2016 *)

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

%Y Cf. A261205, A261206

%Y Subsequence of A006446 and A261342.

%K nonn,more

%O 1,2

%A _Max Alekseyev_, Aug 15 2015