1Math::NumSeq::TotientStUespesrSuCmo(n3t)ributed Perl DocMuamtehn:t:aNtuimoSneq::TotientStepsSum(3)
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NAME

6       Math::NumSeq::TotientStepsSum -- sum of repeated totients to reach 1
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SYNOPSIS

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

14       The sum of the totients on repeatedly applying the totient function to
15       reach 1.
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17           1, 3, 6, 7, 12, 9, 16, 15, 18, 17, 28, 19, 32, ...
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19       For example i=5 applying the totient function goes 5 -> 4 -> 2 -> 1 so
20       total value=5+4+2+1=12.
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22       The default is to include the initial i itself in the sum.  Option
23       "including_self => 0" excludes, in which case for example i=5 has
24       value=4+2+1=7.
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26           0, 1, 3, 3, 7, 3, 9, 7, 9, 7, 17, 7, 19, ...
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28       See Math::NumSeq::TotientPerfect for totient sums equal to i itself.
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FUNCTIONS

31       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
32       classes.
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34       "$seq = Math::NumSeq::TotientStepsSum->new ()"
35           Create and return a new sequence object.
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37   Random Access
38       "$value = $seq->ith($i)"
39           Return the totient steps sum running i down to 1.
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SEE ALSO

42       Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps,
43       Math::NumSeq::TotientPerfect
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HOME PAGE

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

49       Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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51       Math-NumSeq is free software; you can redistribute it and/or modify it
52       under the terms of the GNU General Public License as published by the
53       Free Software Foundation; either version 3, or (at your option) any
54       later version.
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56       Math-NumSeq is distributed in the hope that it will be useful, but
57       WITHOUT ANY WARRANTY; without even the implied warranty of
58       MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
59       General Public License for more details.
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61       You should have received a copy of the GNU General Public License along
62       with Math-NumSeq.  If not, see <http://www.gnu.org/licenses/>.
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66perl v5.34.1                      2022-06-06  Math::NumSeq::TotientStepsSum(3)
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