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a(n) = prime(n)^7.
32

%I #48 Feb 04 2024 01:17:02

%S 128,2187,78125,823543,19487171,62748517,410338673,893871739,

%T 3404825447,17249876309,27512614111,94931877133,194754273881,

%U 271818611107,506623120463,1174711139837,2488651484819,3142742836021,6060711605323

%N a(n) = prime(n)^7.

%C Seventh powers of prime numbers. - _Wesley Ivan Hurt_, Mar 27 2014

%H T. D. Noe, <a href="/A092759/b092759.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Pri#prime_signature">Index to sequences related to prime signature</a>

%F a(n) = A086874(n-1), n>1. - _R. J. Mathar_, Sep 08 2008

%F a(n) = A000040(n)^7 = A001015(A000040(n)). - _Wesley Ivan Hurt_, Mar 27 2014

%F Sum_{n>=1} 1/a(n) = P(7) = 0.0082838328... (A085967). - _Amiram Eldar_, Jul 27 2020

%F From _Amiram Eldar_, Jan 24 2021: (Start)

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

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

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

%p A092759:=n->ithprime(n)^7; seq(A092759(n), n=1..30); # _Wesley Ivan Hurt_, Mar 27 2014

%t Array[Prime[ # ]^7 &, 30] (* _Vladimir Joseph Stephan Orlovsky_, May 01 2008 *)

%t Table[Prime[n]^7, {n, 30}] (* _Wesley Ivan Hurt_, Mar 27 2014 *)

%o (PARI) a(n)=prime(n)^7 \\ _Charles R Greathouse IV_, Jul 20 2011

%o (Magma) [p^7: p in PrimesUpTo(300)]; // _Vincenzo Librandi_, Mar 27 2014

%Y Subsequence of A030626.

%Y Cf. A085967, A013665, A013672.

%K nonn,easy

%O 1,1

%A _Jorge Coveiro_, Apr 13 2004