

A216850


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


1



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
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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: A068629 A144361 A163641 * A070889 A072744 A056042
Adjacent sequences: A216847 A216848 A216849 * A216851 A216852 A216853


KEYWORD

nonn,easy


AUTHOR

Charles R Greathouse IV, Dec 10 2012


STATUS

approved



