NAME
Math::NumSeq::AlmostPrimes  semiprimes and other fixed number of prime factors
SYNOPSIS
use Math::NumSeq::AlmostPrimes;
my $seq = Math::NumSeq::AlmostPrimes>new (factor_count => 2);
my ($i, $value) = $seq>next;
DESCRIPTION
This sequence is various "almost prime" numbers. These are numbers with a given number of prime factors. The default is 2 prime factors, which are the semiprimes. For example 15 because 15=3*5.
4, 6, 9, 10, 14, 15, 21, 22, 25, 26, 33, 34, 35, ...
# starting i=1
Factor Count
factor_count => $c
controls how many prime factors are to be used. 1 would be the primes themselves (the same as Math::NumSeq::Primes). Or for example factor count 4 is as follows. 60 is present because 60=2*2*3*5 has precisely 4 prime factors.
# factor_count => 4
16, 24, 36, 40, 54, 60, ...
The first number in the sequence is 2^factor_count, being prime factor 2 repeated factor_count many times.
Multiplicity
multiplicity => 'distinct'
asks for products of distinct primes. For the default factor count 2 this means exclude squares like 4=2*2, which leaves
# multiplicity => 'distinct'
6, 10, 14, 15, 21, ...
For other factor counts, multiplicity "distinct" eliminates any numbers with repeated factors, leaving only squarefree numbers. For example factor count 4 becomes
# factor_count => 4, multiplicity => 'distinct'
210, 330, 390, 462, 510, 546, ...
For multiplicity "distinct" the first value in the sequence is a primorial (see Math::NumSeq::Primorials), being the first factor_count
many primes multiplied together. For example 210 above is primorial 2*3*5*7.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::AlmostPrimes>new ()
$seq = Math::NumSeq::AlmostPrimes>new (factor_count => $integer, multiplicity => $str)

Create and return a new sequence object.
multiplicity
can be"repeated" repeated primes allowed (the default) "distinct" all primes must be distinct
$bool = $seq>pred($value)

Return true if
$value
is an almostprime, ie. it has exactlyfactor_count
many prime factors, and ifdistinct
is true then all those factors different.This check requires factorizing
$value
and in the current code a hard limit of 2**32 is placed on values to be checked, in the interests of not going into a nearinfinite loop.
SEE ALSO
Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::PrimeFactorCount
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/>.