Giuga numbers: Difference between revisions
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* [[oeis:A007850|OEIS:A007850 - Giuga numbers]] |
* [[oeis:A007850|OEIS:A007850 - Giuga numbers]] |
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=={{header|Julia}}== |
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<lang ruby>using Primes |
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isGiuga(n) = (f = factor(Vector, n); first(f) != n && all(f -> rem(n ÷ f - 1, f) == 0, f)) |
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function getGiuga(N) |
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gcount = 0 |
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for i in 4:typemax(Int) |
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if isGiuga(i) |
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println(i) |
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(gcount += 1) >= N && break |
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end |
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end |
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end |
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getGiuga(4) |
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</lang>{{out}} |
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<pre> |
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30 |
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858 |
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1722 |
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66198 |
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</pre> |
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=={{header|Perl}}== |
=={{header|Perl}}== |
Revision as of 19:25, 1 July 2022
- Definition
A Giuga number is a composite number n which is such that each of its distinct prime factors f divide (n/f - 1) exactly.
All known Giuga numbers are even though it is not known for certain that there are no odd examples.
- Example
30 is a Giuga number because its distinct prime factors are 2, 3 and 5 and:
- 30/2 - 1 = 14 is divisible by 2
- 30/3 - 1 = 9 is divisible by 3
- 30/5 - 1 = 5 is divisible by 5
- Task
Determine and show here the first four Giuga numbers.
- Stretch
Determine the fifth Giuga number and any more you have the patience for.
- References
Julia
<lang ruby>using Primes
isGiuga(n) = (f = factor(Vector, n); first(f) != n && all(f -> rem(n ÷ f - 1, f) == 0, f))
function getGiuga(N)
gcount = 0 for i in 4:typemax(Int) if isGiuga(i) println(i) (gcount += 1) >= N && break end end
end
getGiuga(4)
</lang>
- Output:
30 858 1722 66198
Perl
<lang perl>#!/usr/bin/perl
use strict; # https://rosettacode.org/wiki/Giuga_numbers use warnings; use ntheory qw( factor forcomposites ); use List::Util qw( all );
forcomposites
{ my $n = $_; all { ($n / $_ - 1) % $_ == 0 } factor $n and print "$n\n"; } 4, 67000;</lang>
- Output:
30 858 1722 66198
Wren
Simple brute force but assumes all Giuga numbers will be even, must be square-free and can't be semi-prime.
Takes only about 0.1 seconds to find the first four Giuga numbers but finding the fifth would take many hours using this approach, so I haven't bothered. Hopefully, someone can come up with a better method. <lang ecmascript>import "./math" for Int import "./seq" for Lst
var limit = 4 var giuga = [] var n = 4 while (giuga.count < limit) {
var factors = Int.primeFactors(n) var c = factors.count if (c > 2) { var factors2 = Lst.prune(factors) if (c == factors2.count && factors2.all { |f| (n/f - 1) % f == 0 }) { giuga.add(n) } } n = n + 2
} System.print("The first %(limit) Giuga numbers are:") System.print(giuga)</lang>
- Output:
The first 4 Giuga numbers are: [30, 858, 1722, 66198]