1Math::NumSeq::PrimeFactUosreCrouCnotn(t3r)ibuted Perl DoMcautmhe:n:tNautmiSoenq::PrimeFactorCount(3)
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NAME

6       Math::NumSeq::PrimeFactorCount -- how many prime factors
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SYNOPSIS

9        use Math::NumSeq::PrimeFactorCount;
10        my $seq = Math::NumSeq::PrimeFactorCount->new;
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       The sequence of how many prime factors in i, being
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16           0, 1, 1, 2, 1, 2, ...
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18       The sequence starts from i=1 and 1 is taken to have no prime factors.
19       Then i=2 and i=3 are themselves primes, so 1 prime factor.  Then i=4 is
20       2*2 which is 2 prime factors.
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22       The "multiplicity => "distinct"" option can control whether repeats of
23       a prime factors are counted, or only distinct primes.  For example with
24       "distinct" i=4=2*2 is just 1 prime factor.
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FUNCTIONS

27       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
28       classes.
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30       "$seq = Math::NumSeq::PrimeFactorCount->new ()"
31       "$seq = Math::NumSeq::PrimeFactorCount->new (multiplicity => $str,
32       prime_type => $str)"
33           Create and return a new sequence object.
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35           Option "multiplicity" is a string either
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37               "repeated"      count repeats of primes (the default)
38               "distinct"      count only distinct primes
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40           Option "prime_type" is a string either
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42               "all"           count all primes
43               "odd"           count only odd primes (ie. not 2)
44               "4k+1"          count only primes 4k+1
45               "4k+3"          count only primes 4k+3
46               "twin"          count only twin primes
47                                 (P for which P+2 or P-2 also prime)
48               "SG"            count only Sophie Germain primes
49                                 (P for which 2P+1 also prime)
50               "safe"          count only "safe" primes
51                                 (P for which (P-1)/2 also prime)
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53           "twin" counts both primes of each twin prime pair, so all of 3,5,7,
54           11,13, 17,19, etc.
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56   Random Access
57       "$value = $seq->ith($i)"
58           Return the number of prime factors in $i.
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60           This calculation requires factorizing $i and in the current code
61           after small factors a hard limit of 2**32 is enforced in the
62           interests of not going into a near-infinite loop.
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64       "$bool = $seq->pred($value)"
65           Return true if $value occurs in the sequence, which means simply
66           integer "$value >= 0".
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SEE ALSO

69       Math::NumSeq, Math::NumSeq::Primes, Math::NumSeq::TwinPrimes,
70       Math::NumSeq::SophieGermainPrimes, Math::NumSeq::LiouvilleFunction,
71       Math::NumSeq::MobiusFunction, Math::NumSeq::PowerFlip
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HOME PAGE

74       <http://user42.tuxfamily.org/math-numseq/index.html>
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LICENSE

77       Copyright 2010, 2011, 2012, 2013, 2014, 2016, 2018, 2019 Kevin Ryde
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79       Math-NumSeq is free software; you can redistribute it and/or modify it
80       under the terms of the GNU General Public License as published by the
81       Free Software Foundation; either version 3, or (at your option) any
82       later version.
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84       Math-NumSeq is distributed in the hope that it will be useful, but
85       WITHOUT ANY WARRANTY; without even the implied warranty of
86       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
87       General Public License for more details.
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89       You should have received a copy of the GNU General Public License along
90       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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94perl v5.32.1                      2021-01-27 Math::NumSeq::PrimeFactorCount(3)
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