1Math::NumSeq::DuffinianUNsuemrbeCrosn(t3r)ibuted Perl DoMcautmhe:n:tNautmiSoenq::DuffinianNumbers(3)
2
3
4

NAME

6       Math::NumSeq::DuffinianNumbers -- no common factor with sum of divisors
7

SYNOPSIS

9        use Math::NumSeq::DuffinianNumbers;
10        my $seq = Math::NumSeq::DuffinianNumbers->new ();
11        my ($i, $value) = $seq->next;
12

DESCRIPTION

14       This is the Duffinian numbers which are composites having no common
15       factor with their sum of divisors.
16
17           4, 8, 9, 16, 21, 25, 27, 32, 35, 36, 39, 49, 50, 55, 57, 63, ...
18           starting i=1
19
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.
24

FUNCTIONS

26       See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence
27       classes.
28
29       "$seq = Math::NumSeq::DuffinianNumbers->new ()"
30           Create and return a new sequence object.
31
32       "$bool = $seq->pred($value)"
33           Return true if $value is a Duffinian number.
34
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.
38

SEE ALSO

40       Math::NumSeq
41

HOME PAGE

43       <http://user42.tuxfamily.org/math-numseq/index.html>
44

LICENSE

46       Copyright 2012, 2013, 2014 Kevin Ryde
47
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.
52
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.
57
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/>.
60
61
62
63perl v5.28.0                      2014-06-29 Math::NumSeq::DuffinianNumbers(3)
Impressum