NAME
Math::NumSeq::TotientPerfect  sum of repeated totients is N itself
SYNOPSIS
use Math::NumSeq::TotientPerfect;
my $seq = Math::NumSeq::TotientPerfect>new;
my ($i, $value) = $seq>next;
DESCRIPTION
Numbers for which the sum of repeated totients until reaching 1 gives the starting n itself.
3, 9, 15, 27, 39, 81, 111, 183, 243, 255, ...
For example totient(15)=8, totient(8)=4, totient(4)=2 and totient(1)=1. Adding them up 8+4+2+1=15 so 15 is a perfect totient.
The current implementation of next()
is merely a search by pred()
through all odd integers, which isn't very fast.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::TotientPerfect>new ()

Create and return a new sequence object.
$bool = $seq>pred($value)

Return true if
$value
is a perfect totient.
SEE ALSO
Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014 Kevin Ryde
MathNumSeq 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.
MathNumSeq 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 MathNumSeq. If not, see <http://www.gnu.org/licenses/>.