NAME

Math::NumSeq::LiouvilleFunction -- Liouville function sequence

SYNOPSIS

use Math::NumSeq::LiouvilleFunction;
my $seq = Math::NumSeq::LiouvilleFunction->new;
my ($i, $value) = $seq->next;

DESCRIPTION

The Liouville function, 1, -1, -1, 0, -1, 1, etc, being

1   if i has an even number of prime factors
-1  if i has an odd number of prime factors

The sequence starts from i=1 which is taken to be no prime factors, ie. zero, which is even, hence Liouville function 1. Then i=2 and i=3 are -1 since they have one prime factor (they're primes), and i=4 is value 1 because it's 2*2 which is an even number of prime factors (two 2s).

FUNCTIONS

$seq = Math::NumSeq::LiouvilleFunction->new (key=>value,...)

Create and return a new sequence object.

$value = $seq->ith($i)

Return the Liouville function of $i, being 1 or -1 according to the number of prime factors in $i.

$bool = $seq->pred($value)

Return true if $value is 1 or -1.

SEE ALSO

Math::NumSeq, Math::NumSeq::MobiusFunction, Math::NumSeq::PrimeFactorCount

HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE

Copyright 2010, 2011 Kevin Ryde

Math-NumSeq 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.

Math-NumSeq 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 Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.