Math::NumSeq::TotientPerfect -- sum of repeated totients is N itself
use Math::NumSeq::TotientPerfect; my $seq = Math::NumSeq::TotientPerfect->new; my ($i, $value) = $seq->next;
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.
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.
Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps
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.
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