NAME
Math::NumSeq::PrimeFactorCount  how many prime factors
SYNOPSIS
use Math::NumSeq::PrimeFactorCount;
my $seq = Math::NumSeq::PrimeFactorCount>new;
my ($i, $value) = $seq>next;
DESCRIPTION
The sequence of how many prime factors in i, being
0, 1, 1, 2, 1, 2, ...
The sequence starts from i=1 and 1 is taken to have no prime factors. Then i=2 and i=3 are themselves primes, so 1 prime factor. Then i=4 is 2*2 which is 2 prime factors.
The multiplicity => "distinct"
option can control whether repeats of a prime factors are counted, or only distinct primes. For example with "distinct" i=4=2*2 is just 1 prime factor.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::PrimeFactorCount>new ()
$seq = Math::NumSeq::PrimeFactorCount>new (multiplicity => $str, prime_type => $str)

Create and return a new sequence object.
Option
multiplicity
is a string either"repeated" count repeats of primes (the default) "distinct" count only distinct primes
Option
prime_type
is a string either"all" count all primes "odd" count only odd primes (ie. not 2) "4k+1" count only primes 4k+1 "4k+3" count only primes 4k+3 "twin" count only twin primes (P for which P+2 or P2 also prime) "SG" count only Sophie Germain primes (P for which 2P+1 also prime) "safe" count only "safe" primes (P for which (P1)/2 also prime)
"twin" counts both primes of each twin prime pair, so all of 3,5,7, 11,13, 17,19, etc.
Random Access
$value = $seq>ith($i)

Return the number of prime factors in
$i
.This calculation requires factorizing
$i
and in the current code after small factors a hard limit of 2**32 is enforced in the interests of not going into a nearinfinite loop. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence, which means simply integer$value >= 0
.
SEE ALSO
Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::TwinPrimes, Math::NumSeq::SophieGermainPrimes, Math::NumSeq::LiouvilleFunction, Math::NumSeq::MobiusFunction, Math::NumSeq::PowerFlip
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2018, 2019, 2020 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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 MathNumSeq. If not, see <http://www.gnu.org/licenses/>.