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%I #56 Feb 04 2024 01:12:57
%S 1024,59049,9765625,282475249,25937424601,137858491849,2015993900449,
%T 6131066257801,41426511213649,420707233300201,819628286980801,
%U 4808584372417849,13422659310152401
%N Numbers with 11 divisors.
%C Let p be a prime. Then the n-th number with p divisors is equal to prime(n)^(p-1). - _Omar E. Pol_, May 06 2008
%H R. J. Mathar, <a href="/A030629/b030629.txt">Table of n, a(n) for n = 1..1000</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Index_entries_for_number_of_divisors">Index entries for number of divisors</a>
%F a(n) = A000040(n)^10, i.e. tenth power of n-th prime. - _Henry Bottomley_, Aug 20 2001
%F From _Amiram Eldar_, Jan 24 2021: (Start)
%F Product_{n>=1} (1 + 1/a(n)) = zeta(10)/zeta(20) = 16368226875/(174611*Pi^10) = A013668/A013678.
%F Product_{n>=1} (1 - 1/a(n)) = 1/zeta(10) = 93555/Pi^10 = 1/A013668. (End)
%t (Prime@Range@30)^10 (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)
%o (Sage)
%o [p**10 for p in prime_range(100)]
%o # _Zerinvary Lajos_, May 16 2007
%o (Magma) [p^10: p in PrimesUpTo(300)]; // _Vincenzo Librandi_, Mar 27 2014
%o (PARI) is(n)=isprimepower(n)==10 \\ _Charles R Greathouse IV_, Jun 19 2016
%Y Cf. A000005, A000040, A001248, A008454, A009087, A030514, A030516.
%Y Cf. A013668, A013678.
%K nonn,easy
%O 1,1
%A _Jeff Burch_
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