1Math::NumSeq::Powerful(U3s)er Contributed Perl DocumentatMiaotnh::NumSeq::Powerful(3)
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NAME

6       Math::NumSeq::Powerful -- numbers with certain prime powers
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SYNOPSIS

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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DESCRIPTION

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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FUNCTIONS

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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SEE ALSO

62       Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Cubes,
63       Math::NumSeq::PowerPart
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HOME PAGE

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

69       Copyright 2011, 2012, 2013, 2014, 2015 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.
75
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 v5.28.1                      2015-06-14         Math::NumSeq::Powerful(3)
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