A092759 a(n) = prime(n)^7.

128, 2187, 78125, 823543, 19487171, 62748517, 410338673, 893871739, 3404825447, 17249876309, 27512614111, 94931877133, 194754273881, 271818611107, 506623120463, 1174711139837, 2488651484819, 3142742836021, 6060711605323

Offset: 1

Author

Jorge Coveiro, Apr 13 2004

Keywords

• nonn
• easy

Comments

Seventh powers of prime numbers. - Wesley Ivan Hurt, Mar 27 2014

Examples

			a(1) = 128 since the seventh power of the first prime is 2^7 = 128. - _Wesley Ivan Hurt_, Mar 27 2014
		

Links

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

Crossrefs

Subsequence of A030626.

Cf. A085967, A013665, A013672.

Programs

Magma

[p^7: p in PrimesUpTo(300)]; // Vincenzo Librandi, Mar 27 2014

Maple

A092759:=n->ithprime(n)^7; seq(A092759(n), n=1..30); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

Array[Prime[ # ]^7 &, 30] (* Vladimir Joseph Stephan Orlovsky, May 01 2008 *)
Table[Prime[n]^7, {n, 30}] (* Wesley Ivan Hurt, Mar 27 2014 *)

PARI

a(n)=prime(n)^7 \\ Charles R Greathouse IV, Jul 20 2011

Formula

a(n) = A086874(n-1), n>1. - R. J. Mathar, Sep 08 2008

a(n) = A000040(n)^7 = A001015(A000040(n)). - Wesley Ivan Hurt, Mar 27 2014

Sum_{n>=1} 1/a(n) = P(7) = 0.0082838328... (A085967). - Amiram Eldar, Jul 27 2020

From Amiram Eldar, Jan 24 2021: (Start)

Product_{n>=1} (1 + 1/a(n)) = zeta(7)/zeta(14) = A013665/A013672.

Product_{n>=1} (1 - 1/a(n)) = 1/zeta(7) = 1/A013665. (End)