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%I #57 Oct 27 2023 22:00:43
%S 4,8,32,128,2048,8192,131072,524288,8388608,536870912,2147483648,
%T 137438953472,2199023255552,8796093022208,140737488355328,
%U 9007199254740992,576460752303423488,2305843009213693952
%N a(n) = 2^(n-th prime).
%C These are the "outputs" in Conway's PRIMEGAME (see A007542). - _Alonso del Arte_, Jan 03 2011
%C Multiplicative encoding of the n-th prime. - _Daniel Forgues_, Feb 26 2017
%H Vincenzo Librandi, <a href="/A034785/b034785.txt">Table of n, a(n) for n = 1..200</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F From _Amiram Eldar_, Aug 11 2020: (Start)
%F a(n) = 2^A000040(n).
%F Sum_{n>=1} 1/a(n) = A051006. (End)
%F From _Amiram Eldar_, Nov 22 2022: (Start)
%F Product_{n>=1} (1 + 1/a(n)) = A184083.
%F Product_{n>=1} (1 - 1/a(n)) = A184082. (End)
%e a(4) = 128 because the fourth prime number is 7 and 2^7 = 128.
%t 2^Prime@Range@40 (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)
%o (Haskell)
%o a034785 = (2 ^) . a000040
%o -- _Reinhard Zumkeller_, Feb 07 2015, Jan 24 2012
%o (PARI) a(n)=1<<prime(n) \\ _Charles R Greathouse IV_, Apr 07 2012
%o (Magma) [2^p: p in PrimesUpTo(100)]; // _Vincenzo Librandi_, Apr 29 2014
%Y Cf. A000040, A000430, A051006, A073718 (2^(n-th composite)), A074736.
%Y Cf. A184082, A184083.
%K easy,nonn
%O 1,1
%A _Asher Auel_
%E More terms from _James A. Sellers_, Feb 04 2000
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