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.

1, 4, 27, 16, 3125, 48, 823543, 256, 19683, 320, 285311670611, 162, 302875106592253, 1568, 5625, 65536, 827240261886336764177, 432, 1978419655660313589123979, 2500, 50421, 22528, 20880467999847912034355032910567, 972, 298023223876953125, 70304

Offset: 1

Author

Leroy Quet, Jul 24 2006

Keywords

• nonn

Comments

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]

Examples

			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.
		

Links

• Hagen von Eitzen and Robert Israel, Table of n, a(n) for n = 1..388 (n = 1..50 from Hagen von Eitzen)

Programs

Maple

f:= proc(n)
  local P, r, Cands, j, B;
  P:= sort(convert(numtheory:-factorset(n),list));
  r:= convert(P,`*`);
  Cands:= [seq(r*P[1]^i,i=0..n-1)];
  for j from 2 to nops(P) do
    B:= Cands[n];
    Cands:= sort(map(c -> seq(c*P[j]^i,i=0..floor(log[P[j]](B/c))), Cands));
    Cands:= Cands[1..n];
  od;
  Cands[n]
end proc:
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Oct 09 2016

Mathematica

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]]];
f[1] = 1;
f /@ Range[100] (* Jean-François Alcover, Sep 17 2020, after Robert Israel *)

Extensions

More terms from Joshua Zucker, Aug 12 2006

More terms copied from b-file by Hagen von Eitzen, Jul 20 2009