How to resolve the algorithm Weird numbers step by step in the Wren programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Weird numbers step by step in the Wren programming language
Table of Contents
Problem Statement
In number theory, a weird number is a natural number that is abundant but not semiperfect (and therefore not perfect either). In other words, the sum of the proper divisors of the number (divisors including 1 but not itself) is greater than the number itself (the number is abundant), but no subset of those divisors sums to the number itself (the number is not semiperfect). For example:
Find and display, here on this page, the first 25 weird numbers.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Weird numbers step by step in the Wren programming language
Source code in the wren programming language
import "/math" for Int, Nums
import "/iterate" for Stepped
var semiperfect // recursive
semiperfect = Fn.new { |n, divs|
var le = divs.count
if (le == 0) return false
var h = divs[0]
if (n == h) return true
if (le == 1) return false
var t = divs[1..-1]
if (n < h) return semiperfect.call(n, t)
return semiperfect.call(n-h, t) || semiperfect.call(n, t)
}
var sieve = Fn.new { |limit|
// 'false' denotes abundant and not semi-perfect.
// Only interested in even numbers >= 2
var w = List.filled(limit, false)
for (j in Stepped.new(6...limit, 6)) w[j] = true // eliminate multiples of 3
for (i in Stepped.new(2...limit, 2)) {
if (!w[i]) {
var divs = Int.properDivisors(i)
var sum = Nums.sum(divs)
if (sum <= i) {
w[i] = true
} else if (semiperfect.call(sum-i, divs)) {
for (j in Stepped.new(i...limit, i)) w[j] = true
}
}
}
return w
}
var start = System.clock
var limit = 16313
var w = sieve.call(limit)
var count = 0
var max = 25
System.print("The first 25 weird numbers are:")
var n = 2
while (count < max) {
if (!w[n]) {
System.write("%(n) ")
count = count + 1
}
n = n + 2
}
System.print()
System.print("\nTook %(((System.clock-start)*1000).round) milliseconds")
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