NAME

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

SYNOPSIS

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

DESCRIPTION

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.

FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

$seq = Math::NumSeq::TotientStepsSum->new ()

Create and return a new sequence object.

Random Access

$value = $seq->ith($i)

Return the totient steps sum running i down to 1.

SEE ALSO

Math::NumSeq, Math::NumSeq::Totient, Math::NumSeq::TotientSteps, Math::NumSeq::TotientPerfect

HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

LICENSE

Copyright 2011, 2012, 2013, 2014, 2016, 2019 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/>.