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

1,2

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]

Links

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

Example

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.

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 *)

Crossrefs

Sequence in context: A136511 A218362 A108138 * A133482 A108139 A351365

Adjacent sequences: A119358 A119359 A119360 * A119362 A119363 A119364

Keyword

nonn

Author

Leroy Quet, Jul 24 2006

Extensions

More terms from Joshua Zucker, Aug 12 2006

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

Status

approved