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%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
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