A121067 -id:A121067 - cp's OEIS frontend

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

Leroy Quet, Jul 24 2006

nonn

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]

			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.

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

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

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 *)

More terms from Joshua Zucker, Aug 12 2006

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

A121154 a(n) = the n-th divisor of r(n)^n, where r(n) = (10^n-1)/9 the repunits and the positive divisors of r(n)^n are written in order from smallest to largest.

Original entry on oeis.org

1, 11, 9, 121, 11111, 13, 21613201, 1111, 333, 4961, 219660193449998401, 49, 17530969, 562529, 333, 2057, 79066065031254967758669825213076144489, 91

Offset: 1

Jason Earls, Aug 13 2006

nonn

Sequence continues: r(19)^18, 18491, 1933, 2101917, r(23)^22, 143, 458002801, 161051, 50653, 34001, ... - Charlie Neder, Mar 06 2019

			1, 11, 101, 121, 1111, 1331, 10201, 12221, 14641, 112211, 134431,... is the beginning of the sequence of divisors of 1111^4 and 121 is the 4th term of this sequence, so a(4) = 121.

Charlie Neder, Table of n, a(n) for n = 1..37

Cf. A121067.

a(12)-a(18) from Charlie Neder, Mar 06 2019

A120093 a(n) = the n-th divisor of Fibonacci(n)^n (when the positive divisors of Fibonacci(n)^n are written in order from smallest to largest).

Original entry on oeis.org

1, 0, 4, 27, 625, 32, 4826809, 63, 64, 625, 31181719929966183601, 27, 25601832525455335435322705761, 317057, 80, 343, 1790105629031753086880980667661321707396108307827521, 272, 1975325993

Offset: 1

Jason Earls, Aug 15 2006

nonn

a(2)=0 because Fibonacci(2)^2=1 has no second divisor.

			1, 3, 7, 9, 21, 27, 49, 63, 81, 147, 189, 243, 343, 441, 567, 729,... is the beginning of the sequence of divisors of Fibonacci(8)^8 = 37822859361. 63 is the 8th term, so a(8) = 63.

Cf. A121067.

cp's OEIS Frontend

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.

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A121154 a(n) = the n-th divisor of r(n)^n, where r(n) = (10^n-1)/9 the repunits and the positive divisors of r(n)^n are written in order from smallest to largest.

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A120093 a(n) = the n-th divisor of Fibonacci(n)^n (when the positive divisors of Fibonacci(n)^n are written in order from smallest to largest).

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