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


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


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).


See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::LiouvilleFunction->new ()

Create and return a new sequence object.

Random Access

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

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

This calculation requires factorizing $i and in the current code a hard limit of 2**32 is placed on $i, in the interests of not going into a near-infinite loop.

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

Return true if $value occurs in the sequence, which simply means 1 or -1.


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



Copyright 2010, 2011, 2012 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 <>.