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

512, 19683, 1953125, 40353607, 2357947691, 10604499373, 118587876497, 322687697779, 1801152661463, 14507145975869, 26439622160671, 129961739795077, 327381934393961, 502592611936843, 1119130473102767

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 23 2010

Keywords

• nonn
• easy

Comments

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

Examples

			a(1) = 512 since the ninth power of the first prime is 2^9 = 512. - _Wesley Ivan Hurt_, Mar 27 2014
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Xavier Gourdon and Pascal Sebah, Some Constants from Number theory.
• Will Nicholes, Prime Signatures.

Crossrefs

Cf. A001248, A030078, A030514, A050997, A030516, A092759, A179645.

Cf. A013667, A013676, A085969.

Programs

Magma

[p^9: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

Maple

A179665:=n->ithprime(n)^9; seq(A179665(n), n=1..30); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

Array[Prime[ # ]^9&, 30]
Prime[Range[30]]^9 (* Harvey P. Dale, Jul 20 2024 *)

PARI

a(n)=prime(n)^9 \\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) = A000040(n)^9 = A001017(A000040(n)). - Wesley Ivan Hurt, Mar 27 2014

Sum_{n>=1} 1/a(n) = P(9) = 0.0020044675... (A085969). - Amiram Eldar, Jul 27 2020

From Amiram Eldar, Jan 24 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(9)/zeta(18) = A013667/A013676.

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(9) = 1/A013667. (End)