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.
$value = $seq->ith($i)
Return the Liouville function of
$i, being 1 or -1 according to the number of prime factors in
This calculation requires factorizing
$iand 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
$valueoccurs in the sequence, which simply means 1 or -1.
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.
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