Math::NumSeq::Powerful -- numbers with certain prime powers
use Math::NumSeq::Powerful; my $seq = Math::NumSeq::Powerful->new (powerful_type => 'some', power => 2); my ($i, $value) = $seq->next;
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 4, 8, 9, 12, 16, 18, 20, ... starting i=1
These are the non-squarefrees. The squarefrees have no square factor, and these non-squarefrees 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 or 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.
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.
powerful_type can be
"some" (the default) "all"
power must be 2 or more.
$bool = $seq->pred($value)
Return true if
$value has prime powers of the given type.
Copyright 2011, 2012, 2013, 2014, 2015 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.
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