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%I #40 Aug 11 2020 09:52:53
%S 2,4,16,64,1024,4096,65536,262144,4194304,268435456,1073741824,
%T 68719476736,1099511627776,4398046511104,70368744177664,
%U 4503599627370496,288230376151711744,1152921504606846976
%N Smallest integer for which the number of divisors is the n-th prime.
%C Seems to be the same as "Even numbers with prime number of divisors" - _Jason Earls_, Jul 04 2001
%C Except for the first term, smallest number == 1 (mod prime(n)) having n divisors (by Fermat's little theorem). - _Amarnath Murthy_ and Meenakshi Srikanth (menakan_s(AT)yahoo.com), Jun 20 2003
%H Karl V. Keller, Jr., <a href="/A061286/b061286.txt">Table of n, a(n) for n = 1..460</a>
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>
%F a(n) = 2^(prime(n)-1) = 2^A006093(n).
%F a(n) = A005179(prime(n)). - _R. J. Mathar_, Aug 09 2019
%F Sum_{n>=1} 1/a(n) = A119523. - _Amiram Eldar_, Aug 11 2020
%t Table[2^(p-1),{p,Table[Prime[n],{n,1,18}]}] (* _Geoffrey Critzer_, May 26 2013 *)
%o (PARI) forstep(n=2,100000000,2,x=numdiv(n); if(isprime(x),print(n)))
%o (PARI) a(n)=2^(prime(n)-1) \\ _Charles R Greathouse IV_, Apr 08 2012
%o (Python)
%o from sympy import isprime, divisor_count as tau
%o [2] + [2**(2*n) for n in range(1, 33) if isprime(tau(2**(2*n)))] # _Karl V. Keller, Jr._, Jul 10 2020
%Y Cf. A000005, A005179, A003680, A061283, A061286, A006093, A005097, A006254, A119523, A196202.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, May 22 2001
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