%I #32 May 13 2013 01:54:22

%S 1,2,6,6,30,12,126,30,126,60,2046,60,8190,252,1020,510,131070,252,

%T 524286,1020,16380,4092,8388606,1020,2097150,16380,524286,16380,

%U 536870910,2040,2147483646,131070,4194300,262140,67108860

%N Number of distinct infinite sets of primes congruent to a subset of 1..n mod n.

%H Charles R Greathouse IV, <a href="/A216850/b216850.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = (2^phi(n) - 1)*2^omega(n), where omega(n) is the number of distinct prime factors of n.

%e There are four subsets of {1, 2}: {1, 2}, {1}, {2}, and {}. There are only finitely many primes in {2} or {} mod 2, leaving primes congruent to {1} (the odd primes) and {1, 2} (all primes). Thus a(2) = 2.

%t Table[(2^EulerPhi[n] - 1) 2^PrimeNu[n], {n, 40}] (* _Alonso del Arte_, Dec 10 2012 *)

%o (PARI) a(n)=(2^eulerphi(n)-1)*2^omega(n) \\ _Charles R Greathouse IV_, Dec 10 2012

%K nonn,easy

%O 1,2

%A _Charles R Greathouse IV_, Dec 10 2012