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A179665 a(n) = prime(n)^9.

%I A179665 #57 Jul 20 2024 19:37:08
%S A179665 512,19683,1953125,40353607,2357947691,10604499373,118587876497,
%T A179665 322687697779,1801152661463,14507145975869,26439622160671,
%U A179665 129961739795077,327381934393961,502592611936843,1119130473102767
%N A179665 a(n) = prime(n)^9.
%C A179665 Product_{n >= 2, m_n = (a(n) mod 4) - 2} ((a(n) + 1) / (a(n) - 1))^m_n = 209865342976 / 209844223875. - _Dimitris Valianatos_, May 13 2020
%H A179665 T. D. Noe, <a href="/A179665/b179665.txt">Table of n, a(n) for n = 1..1000</a>
%H A179665 Xavier Gourdon and Pascal Sebah, <a href="http://numbers.computation.free.fr/Constants/Miscellaneous/constantsNumTheory.html">Some Constants from Number theory</a>.
%H A179665 Will Nicholes, <a href="http://willnicholes.com/math/primesiglist.htm">Prime Signatures</a>.
%F A179665 a(n) = A000040(n)^9 = A001017(A000040(n)). - _Wesley Ivan Hurt_, Mar 27 2014
%F A179665 Sum_{n>=1} 1/a(n) = P(9) = 0.0020044675... (A085969). - _Amiram Eldar_, Jul 27 2020
%F A179665 From _Amiram Eldar_, Jan 24 2021: (Start)
%F A179665 Product_{n>=1} (1 + 1/a(n)) = zeta(9)/zeta(18) = A013667/A013676.
%F A179665 Product_{n>=1} (1 - 1/a(n)) = 1/zeta(9) = 1/A013667. (End)
%e A179665 a(1) = 512 since the ninth power of the first prime is 2^9 = 512. - _Wesley Ivan Hurt_, Mar 27 2014
%p A179665 A179665:=n->ithprime(n)^9; seq(A179665(n), n=1..30); # _Wesley Ivan Hurt_, Mar 27 2014
%t A179665 Array[Prime[ # ]^9&, 30]
%t A179665 Prime[Range[30]]^9 (* _Harvey P. Dale_, Jul 20 2024 *)
%o A179665 (PARI) a(n)=prime(n)^9 \\ _Charles R Greathouse IV_, Jul 20 2011
%o A179665 (Magma) [p^9: p in PrimesUpTo(300)]; // _Vincenzo Librandi_, Mar 27 2014
%Y A179665 Cf. A001248, A030078, A030514, A050997, A030516, A092759, A179645.
%Y A179665 Cf. A013667, A013676, A085969.
%K A179665 nonn,easy
%O A179665 1,1
%A A179665 _Vladimir Joseph Stephan Orlovsky_, Jul 23 2010