Kevin Ryde > Math-NumSeq > Math::NumSeq::TotientPerfect

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Module Version: 71   Source  

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/math-numseq/index.html

LICENSE ^

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/>.

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