NAME
Math::NumSeq::MobiusFunction  Mobius function sequence
SYNOPSIS
use Math::NumSeq::MobiusFunction;
my $seq = Math::NumSeq::MobiusFunction>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The sequence of the Mobius function, 1, 1, 1, 0, 1, 1, etc,
1 if i has an even number of distinct prime factors
1 if i has an odd number of distinct prime factors
0 if i has a repeated prime factor
The sequence starts from i=1 and it's reckoned as no prime factors, ie. 0 factors, which is considered even, hence Mobius function 1. Then i=2 and i=3 are value 1 since they have one prime factor (they're primes), and i=4 is value 0 because it's 2*2 which is a repeated prime 2.
FUNCTIONS
$seq = Math::NumSeq::MobiusFunction>new (key=>value,...)

Create and return a new sequence object.
$value = $seq>ith($i)

Return the Mobius function of
$i
, being 1, 0 or 1 according to the prime factors of$i
. $bool = $seq>pred($value)

Return true if
$value
is 1, 0 or 1.
SEE ALSO
Math::NumSeq, Math::NumSeq::LiouvilleFunction, Math::NumSeq::PrimeFactorCount
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011 Kevin Ryde
MathNumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.
MathNumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with MathNumSeq. If not, see <http://www.gnu.org/licenses/>.