NAME
Math::NumSeq::Powerful  numbers with certain prime powers
SYNOPSIS
use Math::NumSeq::Powerful;
my $seq = Math::NumSeq::Powerful>new (powerful_type => 'some',
power => 2);
my ($i, $value) = $seq>next;
DESCRIPTION
This is integers with a minimum prime power. The powerful_type
option (a string) can be
"some" some exp >= power
"all" all exp >= power
The default is "some" and power=2, which means there must be some prime factor which is a square or higher,
# default powerful_type="some" power=2
# starting i=1
4, 8, 9, 12, 16, 18, 20, ...
These are the nonsquarefrees. The squarefrees have no square factor, and these nonsquarefrees have at least one square factor. (Sometimes this is called "squareful" but this can be confused with the "all" style where all primes must be a square of better.)
The "all" option with power=2 demands that all primes are square or higher.
powerful_type="all" power=2
1, 4, 8, 9, 16, 25, 27, 32, 36, ...
Notice for example 12=2*2*3 is excluded because its prime factor 3 is not squared or better. 1 is included on the basis that it has no prime factors to check the power of.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::Powerful>new (powerful_type => $str, power => $integer)

Create and return a new sequence object.
$bool = $seq>pred($value)

Return true if
$value
has prime powers of the given type.
SEE ALSO
Math::NumSeq, Math::NumSeq::Squares, Math::NumSeq::Cubes, Math::NumSeq::PowerPart
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2011, 2012, 2013 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/>.