1Math::NumSeq::DuffinianUNsuemrbeCrosn(t3r)ibuted Perl DoMcautmhe:n:tNautmiSoenq::DuffinianNumbers(3)
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6 Math::NumSeq::DuffinianNumbers -- no common factor with sum of divisors
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9 use Math::NumSeq::DuffinianNumbers;
10 my $seq = Math::NumSeq::DuffinianNumbers->new ();
11 my ($i, $value) = $seq->next;
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14 This is the Duffinian numbers which are composites having no common
15 factor with their sum of divisors.
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17 4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, ...
18 starting i=1
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20 For example 21 has divisors 1,3,7,21 total 32 which has no common
21 factor with 21. Only composites are included since primes would not be
22 particularly interesting for this rule. They'd having only divisors
23 1,p and so p+1 never having a common factor with p.
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26 See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
27 classes.
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29 "$seq = Math::NumSeq::DuffinianNumbers->new ()"
30 Create and return a new sequence object.
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32 "$bool = $seq->pred($value)"
33 Return true if $value is a Duffinian number.
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35 In the current code a hard limit of 2**32 is placed on the $value
36 to be checked, in the interests of not going into a near-infinite
37 loop. The return is "undef" for bigger values.
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40 Math::NumSeq
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43 <http://user42.tuxfamily.org/math-numseq/index.html>
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46 Copyright 2012, 2013, 2014, 2016, 2019, 2020 Kevin Ryde
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48 Math-NumSeq is free software; you can redistribute it and/or modify it
49 under the terms of the GNU General Public License as published by the
50 Free Software Foundation; either version 3, or (at your option) any
51 later version.
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53 Math-NumSeq is distributed in the hope that it will be useful, but
54 WITHOUT ANY WARRANTY; without even the implied warranty of
55 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
56 General Public License for more details.
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58 You should have received a copy of the GNU General Public License along
59 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
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63perl v5.36.0 2022-07-22 Math::NumSeq::DuffinianNumbers(3)