1Math::NumSeq::PowerPartU(s3e)r Contributed Perl DocumentaMtaitohn::NumSeq::PowerPart(3)
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NAME

6       Math::NumSeq::PowerPart -- largest square root etc divisor
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SYNOPSIS

9        use Math::NumSeq::PowerPart;
10        my $seq = Math::NumSeq::PowerPart->new (power => 2);
11        my ($i, $value) = $seq->next;
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DESCRIPTION

14       This sequence is the largest integer whose square is a divisor of i,
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16           1, 1, 1, 2, 1, 1, 1, 2, 3, ...
17           starting i=1
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19       For example at i=27 the value is 3 since 3^2=9 is the largest square
20       which is a divisor of 27.  Notice the sequence value is the square
21       root, ie. 3, of the divisor, not the square 9.
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23       When i has no square divisor, ie. is square-free, the value is 1.
24       Compare the "MobiusFunction" where value 1 or -1 means square-free.
25       And conversely "MobiusFunction" is 0 when there's a square factor, and
26       PowerPart value here is > 1 in that case.
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28   Power Option
29       The "power" parameter selects what power divisor to seek.  For example
30       "power=>3" finds the largest cube dividing i and the sequence values
31       are the cube roots.
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33           power=>3
34           1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, ...
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36       For example i=24 the value is 2, since 2^3=8 is the largest cube which
37       divides 24.
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FUNCTIONS

40       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
41       classes.
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43       "$seq = Math::NumSeq::PowerPart->new ()"
44       "$seq = Math::NumSeq::PowerPart->new (power => $integer)"
45           Create and return a new sequence object.
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47   Random Access
48       "$value = $seq->ith($i)"
49           Return the largest perfect square, cube, etc root dividing $i.
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51           This calculation requires factorizing $i and in the current code
52           after small factors a hard limit of 2**32 is enforced in the
53           interests of not going into a near-infinite loop.
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55       "$bool = $seq->pred($value)"
56           Return true if $value occurs in the sequence, which is simply any
57           integer "$value >= 1".
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SEE ALSO

60       Math::NumSeq, Math::NumSeq::MobiusFunction, Math::NumSeq::Powerful
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HOME PAGE

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

66       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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68       Math-NumSeq is free software; you can redistribute it and/or modify it
69       under the terms of the GNU General Public License as published by the
70       Free Software Foundation; either version 3, or (at your option) any
71       later version.
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73       Math-NumSeq is distributed in the hope that it will be useful, but
74       WITHOUT ANY WARRANTY; without even the implied warranty of
75       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
76       General Public License for more details.
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78       You should have received a copy of the GNU General Public License along
79       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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83perl v5.36.0                      2023-01-20        Math::NumSeq::PowerPart(3)