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A061286 Smallest integer for which the number of divisors is the n-th prime. 28


%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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Last modified April 10 22:05 EDT 2021. Contains 342856 sequences. (Running on oeis4.)