NAME

Math::NumSeq::DedekindPsiCumulative -- cumulative Psi function

SYNOPSIS

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

DESCRIPTION

The cumulative Dedekind Psi function,

1,4,8,14,20,32,40,52,64,82,94,118,...

The Psi function is

Psi(n) =        product          (p+1) * p^(e-1)
         prime factors p^e in n

The p+1 means one copy of each distinct prime in n is changed from p to p+1. This is similar to Euler's totient function phi(n) (see Math::NumSeq::Totient) but phi(n) changes to p-1 instead of p+1.

FUNCTIONS

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

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

Create and return a new sequence object.

SEE ALSO

Math::NumSeq, Math::NumSeq::DedekindPsiSteps, Math::NumSeq::TotientCumulative

HOME PAGE

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

LICENSE

Copyright 2012 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/>.