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A119361 a(n) is the n-th positive integer which is divisible by the same distinct primes as n and which is divisible by no other primes.

%I A119361 #32 Sep 18 2020 06:04:25
%S A119361 1,4,27,16,3125,48,823543,256,19683,320,285311670611,162,
%T A119361 302875106592253,1568,5625,65536,827240261886336764177,432,
%U A119361 1978419655660313589123979,2500,50421,22528,20880467999847912034355032910567,972,298023223876953125,70304
%N A119361 a(n) is the n-th positive integer which is divisible by the same distinct primes as n and which is divisible by no other primes.
%C A119361 It appears that a(n) is rad(n) times the n-th smallest divisor of n^n, i.e., A007947(n)*A121067(n). [_Hagen von Eitzen_, Jul 20 2009; _Charles R Greathouse IV_, Oct 09 2016]
%H A119361 Hagen von Eitzen and Robert Israel, <a href="/A119361/b119361.txt">Table of n, a(n) for n = 1..388</a> (n = 1..50 from Hagen von Eitzen)
%e A119361 6 = 2*3. The sequence of positive integers which are divisible by 2 and 3, but not divisible by any other primes, is 6,12,18,24,36,48,54,... The 6th such integer is 48, so a(6) = 48.
%p A119361 f:= proc(n)
%p A119361   local P, r, Cands, j, B;
%p A119361   P:= sort(convert(numtheory:-factorset(n),list));
%p A119361   r:= convert(P,`*`);
%p A119361   Cands:= [seq(r*P[1]^i,i=0..n-1)];
%p A119361   for j from 2 to nops(P) do
%p A119361     B:= Cands[n];
%p A119361     Cands:= sort(map(c -> seq(c*P[j]^i,i=0..floor(log[P[j]](B/c))), Cands));
%p A119361     Cands:= Cands[1..n];
%p A119361   od;
%p A119361   Cands[n]
%p A119361 end proc:
%p A119361 f(1):= 1:
%p A119361 map(f, [$1..100]); # _Robert Israel_, Oct 09 2016
%t A119361 f[n_] := Module[{P, r, Cands, j, B}, P = FactorInteger[n][[All, 1]]; r = Times @@ P; Cands = Table[r P[[1]]^i, {i, 0, n-1}]; Do[B = Cands[[n]]; Cands = Table[# P[[j]]^i, {i, 0, Floor[Log[P[[j]], B/#]]}]& /@ Cands // Flatten // Sort; Cands = Cands[[1;;n]], {j, 2, Length[P]}]; Cands[[n]]];
%t A119361 f[1] = 1;
%t A119361 f /@ Range[100] (* _Jean-François Alcover_, Sep 17 2020, after _Robert Israel_ *)
%K A119361 nonn
%O A119361 1,2
%A A119361 _Leroy Quet_, Jul 24 2006
%E A119361 More terms from _Joshua Zucker_, Aug 12 2006
%E A119361 More terms copied from b-file by _Hagen von Eitzen_, Jul 20 2009