Math::NumSeq::DuffinianNumbers -- no common factor with sum of divisors
use Math::NumSeq::DuffinianNumbers; my $seq = Math::NumSeq::DuffinianNumbers->new (); my ($i, $value) = $seq->next;
This is the Duffinian numbers which are composites having no common factor with their sum of divisors.
4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, ... starting i=1
For example 21 has divisors 1,3,7,21 total 32 which has no common factor with 21. Only composites are included since primes would not be particularly interesting for this rule. They'd having only divisors 1,p and so p+1 never having a common factor with p.
See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.
$seq = Math::NumSeq::DuffinianNumbers->new ()
Create and return a new sequence object.
$bool = $seq->pred($value)
Return true if
$valueis a Duffinian number.
In the current code a hard limit of 2**32 is placed on the
$valueto be checked, in the interests of not going into a near-infinite loop. The return is
undeffor bigger values.
Copyright 2012, 2013, 2014, 2016, 2019 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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