1Math::NumSeq::TotientStUespesrSuCmo(n3t)ributed Perl DocMuamtehn:t:aNtuimoSneq::TotientStepsSum(3)
2
3
4

NAME

6       Math::NumSeq::TotientStepsSum -- sum of repeated totients to reach 1
7

SYNOPSIS

9        use Math::NumSeq::TotientStepsSum;
10        my $seq = Math::NumSeq::TotientStepsSum->new;
11        my ($i, $value) = $seq->next;
12

DESCRIPTION

14       The sum of the totients on repeatedly applying the totient function to
15       reach 1.
16
17           1, 3, 6, 7, 12, 9, 16, 15, 18, 17, 28, 19, 32, ...
18
19       For example i=5 applying the totient function goes 5 -> 4 -> 2 -> 1 so
20       total value=5+4+2+1=12.
21
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.
25
26           0, 1, 3, 3, 7, 3, 9, 7, 9, 7, 17, 7, 19, ...
27
28       See Math::NumSeq::TotientPerfect for totient sums equal to i itself.
29

FUNCTIONS

31       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
32       classes.
33
34       "$seq = Math::NumSeq::TotientStepsSum->new ()"
35           Create and return a new sequence object.
36
37   Random Access
38       "$value = $seq->ith($i)"
39           Return the totient steps sum running i down to 1.
40

SEE ALSO

42       Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps,
43       Math::NumSeq::TotientPerfect
44

HOME PAGE

46       <http://user42.tuxfamily.org/math-numseq/index.html>
47

LICENSE

49       Copyright 2011, 2012, 2013, 2014 Kevin Ryde
50
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.
55
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.
60
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/>.
63
64
65
66perl v5.28.0                      2014-06-29  Math::NumSeq::TotientStepsSum(3)
Impressum