NAME
Math::NumSeq::PowerFlip  prime exponent flip
SYNOPSIS
use Math::NumSeq::PowerFlip;
my $seq = Math::NumSeq::PowerFlip>new;
my ($i, $value) = $seq>next;
DESCRIPTION
This sequence is i with primes and exponents flipped in the prime factorization.
i = p^e * q^f * ...
becomes
value = e^p * f^q * ...
which gives
1, 1, 1, 4, 1, 1, 1, 9, 8, 1, 1, 4, 1, 1, 1, 16, 1, 8, 1, 4, ...
starting i=1
For example i=1000=2^3*5^3 becomes value=3^2*3^5=3^7=2187.
Any i=prime has value=1 since i=p^1 becomes value=1^p=1. Value=1 occurs precisely when i=p*q*r*etc with no repeated prime factor, ie. when i is squarefree.
The possible values which occur in the sequence are related to square factors. Since value=e^p has prime p>=2, every e,f,g etc powered up in the value is a square or higher power. So sequence values are a product of squares and higher.
These calculations require 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.
FUNCTIONS
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
Random Access
$value = $seq>ith($i)

Return
$i
with the prime powers and exponents flipped. $bool = $seq>pred($value)

Return true if
$value
occurs in the sequence. As noted above this means an integer$value
with at least one squared prime factor.
SEE ALSO
Math::NumSeq, Math::NumSeq::PrimeFactorCount
HOME PAGE
http://user42.tuxfamily.org/mathnumseq/index.html
LICENSE
Copyright 2012, 2013, 2014, 2016, 2019, 2020 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/>.