A216850 Number of distinct infinite sets of primes congruent to a subset of 1..n mod n.

1, 2, 6, 6, 30, 12, 126, 30, 126, 60, 2046, 60, 8190, 252, 1020, 510, 131070, 252, 524286, 1020, 16380, 4092, 8388606, 1020, 2097150, 16380, 524286, 16380, 536870910, 2040, 2147483646, 131070, 4194300, 262140, 67108860

Offset

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

Formula

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

Example

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.

Mathematica

Table[(2^EulerPhi[n] - 1) 2^PrimeNu[n], {n, 40}] (* Alonso del Arte, Dec 10 2012 *)

Prog

(PARI) a(n)=(2^eulerphi(n)-1)*2^omega(n) \\ Charles R Greathouse IV, Dec 10 2012

Crossrefs

Sequence in context: A163641 A333072 A333196 * A070889 A072744 A056042

Adjacent sequences: A216847 A216848 A216849 * A216851 A216852 A216853

Keyword

nonn,easy

Author

Charles R Greathouse IV, Dec 10 2012

Status

approved