NAME
Math::NumSeq::PowerPart  largest square root etc divisor
SYNOPSIS
use Math::NumSeq::PowerPart;
my $seq = Math::NumSeq::PowerPart>new (power => 2);
my ($i, $value) = $seq>next;
DESCRIPTION
This sequence is the largest integer whose square is a divisor of i,
1, 1, 1, 2, 1, 1, 1, 2, 3, ...
starting i=1
For example at i=27 the value is 3 since 3^2=9 is the largest square which is a divisor of 27. Notice the sequence value is the square root, ie. 3, of the divisor, not the square 9.
When i has no square divisor, ie. is squarefree, the value is 1. Compare the MobiusFunction
where value 1 or 1 means squarefree. And conversely MobiusFunction
is 0 when there's a square factor, and PowerPart value here is > 1 in that case.
Power Option
The power
parameter selects what power divisor to seek. For example power=>3
finds the largest cube dividing i and the sequence values are the cube roots.
power=>3
1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, ...
For example i=24 the value is 2, since 2^3=8 is the largest cube which divides 24.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::PowerPart>new ()
$seq = Math::NumSeq::PowerPart>new (power => $integer)

Create and return a new sequence object.
Random Access
$value = $seq>ith($i)

Return the largest perfect square, cube, etc root dividing
$i
.This calculation requires factorizing
$i
and in the current code after small factors a hard limit of 2**32 is enforced in the interests of not going into a nearinfinite loop. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence, which is simply any integer$value >= 1
.
SEE ALSO
Math::NumSeq, Math::NumSeq::MobiusFunction, Math::NumSeq::Powerful
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013, 2014, 2016, 2019 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/>.