A179645 a(n) = prime(n)^8.

256, 6561, 390625, 5764801, 214358881, 815730721, 6975757441, 16983563041, 78310985281, 500246412961, 852891037441, 3512479453921, 7984925229121, 11688200277601, 23811286661761, 62259690411361, 146830437604321

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jul 21 2010

Keywords

• nonn
• easy

Examples

			a(1) = 256 since the eighth power of the first prime is 2^7 = 256. - _Wesley Ivan Hurt_, Mar 27 2014
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000
• Will Nicholes, Prime Signatures.
• Index to sequences related to prime signature

Crossrefs

Cf. A000040, A001016, A085968.

Cf. A013666, A013674.

Programs

Magma

[p^8: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

Maple

A179645:=n->ithprime(n)^8; seq(A179645(n), n=1..40); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

Array[Prime[ # ]^8&, 40]

PARI

a(n)=prime(n)^8 \\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) = A000040(n)^8 = A001016(A000040(n)). - Wesley Ivan Hurt, Mar 27 2014

Sum_{n>=1} 1/a(n) = P(8) = 0.0040614053... (A085968). - Amiram Eldar, Jul 27 2020

From Amiram Eldar, Jan 24 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(8)/zeta(16) = 34459425/(3617*Pi^8) = A013666/A013674.

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(8) = 9450/Pi^8 = 1/A013666. (End)