Math::NumSeq::MobiusFunction -- Mobius function sequence
use Math::NumSeq::MobiusFunction; my $seq = Math::NumSeq::MobiusFunction->new; my ($i, $value) = $seq->next;
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.
$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
$bool = $seq->pred($value)
Return true if
$valueis 1, 0 or -1.
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/>.