Math::NumSeq::TotientStepsSum -- sum of repeated totients to reach 1
use Math::NumSeq::TotientStepsSum; my $seq = Math::NumSeq::TotientStepsSum->new; my ($i, $value) = $seq->next;
The sum of the totients on repeatedly applying the totient function to reach 1.
1, 3, 6, 7, 12, 9, 16, 15, 18, 17, 28, 19, 32, ...
For example i=5 applying the totient function goes 5 -> 4 -> 2 -> 1 so total value=5+4+2+1=12.
The default is to include the initial i itself in the sum. Option including_self => 0
excludes, in which case for example i=5 has value=4+2+1=7.
0, 1, 3, 3, 7, 3, 9, 7, 9, 7, 17, 7, 19, ...
See Math::NumSeq::TotientPerfect for totient sums equal to i itself.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::TotientStepsSum->new ()
Create and return a new sequence object.
$value = $seq->ith($i)
Return the totient steps sum running i down to 1.
Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps, Math::NumSeq::TotientPerfect
http://user42.tuxfamily.org/math-numseq/index.html
Copyright 2011, 2012, 2013, 2014 Kevin Ryde
Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.
Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.