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, ...
starting i=1
Each value is
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 value=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
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
Random Access
$value = $seq>ith($i)

Return the Mobius function of
$i
, being 1, 0 or 1 according to the prime factors of$i
.This calculation requires factorizing
$i
and in the current code small primes are checked then a hard limit of 2**32 is placed on$i
, in the interests of not going into a nearinfinite loop. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence, which means simply 1, 0 or 1.
SEE ALSO
Math::NumSeq, Math::NumSeq::LiouvilleFunction, Math::NumSeq::PrimeFactorCount
"moebius" in Math::Prime::Util
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2019, 2020 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/>.