Attractive Numbers

This example shows the implementation of an algorithm for finding attractive numbers from 1 to 120.

Introduction

The algorithm of "attractive numbers" is a curious mathematical problem that involves determining natural numbers whose sum of prime factors is a prime number.

What is factorization?

Each natural number can be represented as a product of prime numbers (factors). For example:

The number 12 has prime factors , or a record based on degrees — .

Function factor in Julia, it decomposes the input number exactly like this.

What does the number “attractive" mean?

A number is considered attractive when the sum of allits unique prime factors (without taking into account the degree) is a prime number.

Let's explain:

For the number 12: factorization → [2, 3] ? sum = 2 + 3 = 5.
Since 5 is a prime number, 12 is an attractive number.

We need to find all such numbers in the range from 1 to 120.

Problem solving

Installing the required package

import Pkg; Pkg.add("Primes")

Connecting the module Primes. It provides functions for working with prime numbers, for example, isprime() checks if a number is prime

using Primes

Function isattractive(n) accepts a positive integer n, then:

factor(n) — we get a dictionary of prime divisors with degrees
values(...) — we take only values (ignore degrees)
sum(...) — adding up the values
isprime(...) — are we checking if this amount is simple?

function isattractive(n)
    return isprime(sum(values(factor(n))))
end

isattractive (generic function with 1 method)

Function printattractive(m, n):

accepts two arguments - the boundaries of the range from m before n
causes filtering of the m:n array using the function isattractive()
outputs a beautifully formatted list of numbers via println()

function printattractive(m, n)
    println("Привлекательные числа от $m до $n:\n", filter(isattractive, m:n))
end

printattractive (generic function with 1 method)

Running calculations, the function created above with the specified range is called.

printattractive(1, 120)

Привлекательные числа от 1 до 120:
[4, 6, 8, 9, 10, 12, 14, 15, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 42, 44, 45, 46, 48, 49, 50, 51, 52, 55, 57, 58, 62, 63, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 82, 85, 86, 87, 91, 92, 93, 94, 95, 98, 99, 102, 105, 106, 108, 110, 111, 112, 114, 115, 116, 117, 118, 119, 120]

Conclusion

Using this example, we have learned how to solve an interesting mathematical problem about "attractive" numbers using the features of the Julia programming language. We:

Have you learned how to use the library Primes for working with prime numbers;
Used the built-in function factor() from Base.Math (part of the standard library);
We have written a function that checks whether a number is attractive;
Implemented a convenient way to display the result in the terminal.

This approach demonstrates the elegance and readability of Julia code, especially when combining powerful built-in tools and concise syntax.

The example was developed using materials from Rosetta Code