%I #42 Feb 04 2024 01:13:04

%S 4096,531441,244140625,13841287201,3138428376721,23298085122481,

%T 582622237229761,2213314919066161,21914624432020321,

%U 353814783205469041,787662783788549761,6582952005840035281,22563490300366186081,39959630797262576401,116191483108948578241

%N Numbers with 13 divisors.

%C 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

%H R. J. Mathar, <a href="/A030631/b030631.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A000040(n)^(13-1) = A000040(n)^(12). - _Omar E. Pol_, May 06 2008

%F From _Amiram Eldar_, Jan 24 2021: (Start)

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

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

%t (Prime@Range@30)^12 (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)

%o (Magma) [p^12: p in PrimesUpTo(100)]; // _Vincenzo Librandi_, Mar 27 2014

%o (PARI) is(n)=isprimepower(n)==12 \\ _Charles R Greathouse IV_, Jun 19 2016

%Y Cf. A000040, A013670, A030629.

%Y Subsequence of A008456.

%K nonn,easy

%O 1,1

%A _Jeff Burch_