1Math::NumSeq::Powerful(U3s)er Contributed Perl DocumentatMiaotnh::NumSeq::Powerful(3)
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6 Math::NumSeq::Powerful -- numbers with certain prime powers
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9 use Math::NumSeq::Powerful;
10 my $seq = Math::NumSeq::Powerful->new (powerful_type => 'some',
11 power => 2);
12 my ($i, $value) = $seq->next;
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15 This is integers with a minimum prime power. The "powerful_type"
16 option (a string) can be
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18 "some" some exp >= power
19 "all" all exp >= power
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21 The default is "some" and power=2, which means there must be some prime
22 factor which is a square or higher,
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24 # default powerful_type="some" power=2
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26 4, 8, 9, 12, 16, 18, 20, ...
27 starting i=1
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29 These are the non-squarefrees. The squarefrees have no square factor,
30 and these non-squarefrees have at least one square factor. (Sometimes
31 this is called "squareful" but this can be confused with the "all"
32 style where all primes must be a square or better.)
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34 The "all" option with power=2 demands that all primes are square or
35 higher.
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37 powerful_type="all" power=2
38 1, 4, 8, 9, 16, 25, 27, 32, 36, ...
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40 Notice for example 12=2*2*3 is excluded because its prime factor 3 is
41 not squared or better. 1 is included on the basis that it has no prime
42 factors.
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45 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
46 classes.
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48 "$seq = Math::NumSeq::Powerful->new (powerful_type => $str, power =>
49 $integer)"
50 Create and return a new sequence object. "powerful_type" can be
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52 "some" (the default)
53 "all"
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55 "power" must be 2 or more.
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57 Random Access
58 "$bool = $seq->pred($value)"
59 Return true if $value has prime powers of the given type.
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62 Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Cubes,
63 Math::NumSeq::PowerPart
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66 <http://user42.tuxfamily.org/math-numseq/index.html>
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69 Copyright 2011, 2012, 2013, 2014, 2015, 2016, 2019 Kevin Ryde
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71 Math-NumSeq is free software; you can redistribute it and/or modify it
72 under the terms of the GNU General Public License as published by the
73 Free Software Foundation; either version 3, or (at your option) any
74 later version.
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76 Math-NumSeq is distributed in the hope that it will be useful, but
77 WITHOUT ANY WARRANTY; without even the implied warranty of
78 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
79 General Public License for more details.
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81 You should have received a copy of the GNU General Public License along
82 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
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86perl v5.32.0 2020-07-28 Math::NumSeq::Powerful(3)