Math::NumSeq::PowerPart -- largest square root etc divisor


 use Math::NumSeq::PowerPart;
 my $seq = Math::NumSeq::PowerPart->new (power => 2);
 my ($i, $value) = $seq->next;


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 square-free, the value is 1. Compare the MobiusFunction where value 1 or -1 means square-free. 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.

    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.


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 near-infinite loop.

$bool = $seq->pred($value)

Return true if $value occurs in the sequence, which is simply any integer $value >= 1.


Math::NumSeq, Math::NumSeq::MobiusFunction, Math::NumSeq::Powerful



Copyright 2011, 2012, 2013, 2014, 2016, 2019, 2020 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.

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