A119319 -id:A119319 - cp's OEIS frontend

A119317 n-th divisor of A087134(n), the smallest number whose n-th divisor is prime (for n > 1).

1, 2, 3, 5, 7, 7, 13, 13, 19, 17, 23, 31, 29, 31, 41, 61, 61, 61, 47, 61, 73, 97, 127, 71, 97, 107, 127, 149, 173, 211, 127, 97, 107, 211, 127, 149, 173, 181, 211, 257, 281, 317, 181, 421, 241, 257, 281, 317, 337, 367, 421, 509, 563, 631, 727, 421, 487, 509

Offset: 1

Reinhard Zumkeller, May 15 2006

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000040, A119318, A119319.

a[1] = 1; a[n_] := Module[{k = 1, d}, While[DivisorSigma[0, k] < n || ! PrimeQ[d = Divisors[k][[n]]], k++]; d]; Array[a, 30]  (* Amiram Eldar, Feb 06 2019 *)

A119317(n) := block(
   if equal(n,1) then
      return(1),
   for i : 1 do (
      idv : listify(divisors(i)),
      if length(idv) >= n then (
         if primep(idv[n]) then
            return(idv[n])
        )
     )
)$ /* R. J. Mathar, Mar 13 2012 */

More terms from Amiram Eldar, Feb 06 2019

A119318 n-th divisor of A119311(n), the smallest number such that the n-th divisor is a prime power.

Original entry on oeis.org

1, 2, 4, 8, 16, 8, 27, 16, 27, 32, 27, 64, 27, 128, 32, 256, 81, 128, 64, 1024, 256, 128, 128, 512, 243, 256, 256, 128, 128, 512, 512, 128, 256, 128, 256, 243, 343, 729, 729, 512, 512, 256, 4096, 729, 1024, 729, 1024, 512, 256, 512, 729, 2048, 256, 1024, 1024

Offset: 1

Reinhard Zumkeller, May 15 2006

nonn

Not all terms are powers of 2 or of 3, see example.

			n=37: the set of divisors of A119311(37) = 41160 has
tau(41160) = 64 elements: {1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 15, 20, 21, 24, 28, 30, 35, 40, 42, 49, 56, 60, 70, 84, 98, 105, 120, 140, 147, 168, 196, 210, 245, 280, 294, [[343]], 392, 420, 490, 588, 686, ...}; the 37th divisor of 41160 = a(37) = 343 = 7^3.

Cf. A119317, A119319.

cp's OEIS Frontend

A119317 n-th divisor of A087134(n), the smallest number whose n-th divisor is prime (for n > 1).

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A119318 n-th divisor of A119311(n), the smallest number such that the n-th divisor is a prime power.

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