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Kevin Ryde > Math-NumSeq > Math::NumSeq::MobiusFunction

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Module Version: 72

# 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.

`\$seq = Math::NumSeq::MobiusFunction->new ()`

Create and return a new sequence object.

## 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 near-infinite loop.

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

Return true if `\$value` occurs in the sequence, which means simply 1, 0 or -1.

"moebius" in Math::Prime::Util

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

Copyright 2010, 2011, 2012, 2013, 2014 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/>.

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