A030631 Numbers with 13 divisors.

4096, 531441, 244140625, 13841287201, 3138428376721, 23298085122481, 582622237229761, 2213314919066161, 21914624432020321, 353814783205469041, 787662783788549761, 6582952005840035281, 22563490300366186081, 39959630797262576401, 116191483108948578241

Offset: 1

Author

Jeff Burch

Keywords

• nonn
• easy

Comments

12th powers of primes. The n-th number with p divisors is equal to the n-th prime raised to power p-1, where p is prime. - Omar E. Pol, May 06 2008

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A013670, A030629.

Subsequence of A008456.

Programs

Magma

[p^12: p in PrimesUpTo(100)]; // Vincenzo Librandi, Mar 27 2014

Mathematica

(Prime@Range@30)^12  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

PARI

is(n)=isprimepower(n)==12 \\ Charles R Greathouse IV, Jun 19 2016

Formula

a(n) = A000040(n)^(13-1) = A000040(n)^(12). - Omar E. Pol, May 06 2008

From Amiram Eldar, Jan 24 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(12)/zeta(24) = 218517792968475/(236364091*Pi^12).

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(12) = 638512875/(691*Pi^12) = 1/A013670. (End)