How to resolve the algorithm Amicable pairs step by step in the Cowgol programming language

Published on 12 May 2024 09:40 PM
#Cowgol

How to resolve the algorithm Amicable pairs step by step in the Cowgol programming language

Table of Contents

Problem Statement

Two integers

N

{\displaystyle N}

and

M

{\displaystyle M}

are said to be amicable pairs if

N ≠ M

{\displaystyle N\neq M}

and the sum of the proper divisors of

N

{\displaystyle N}

(

s u m

(

p r o p D i v s

( N ) )

{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}

)

= M

{\displaystyle =M}

as well as

s u m

(

p r o p D i v s

( M ) )

N

{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}

.

1184 and 1210 are an amicable pair, with proper divisors:

Calculate and show here the Amicable pairs below 20,000; (there are eight).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Amicable pairs step by step in the Cowgol programming language

Source code in the cowgol programming language

include "cowgol.coh";

const LIMIT := 20000;

# Calculate sums of proper divisors
var divSum: uint16[LIMIT + 1];
var i: @indexof divSum;
var j: @indexof divSum;

i := 2;
while i <= LIMIT loop
    divSum[i] := 1;
    i := i + 1;
end loop;

i := 2;
while i <= LIMIT/2 loop
    j := i * 2;
    while j <= LIMIT loop
        divSum[j] := divSum[j] + i;
        j := j + i;
    end loop;
    i := i + 1;
end loop;

# Test each pair
i := 2;
while i <= LIMIT loop
    j := i + 1;
    while j <= LIMIT loop
        if divSum[i] == j and divSum[j] == i then
            print_i32(i as uint32);
            print(", ");
            print_i32(j as uint32);
            print_nl();
        end if;
        j := j + 1;
    end loop;
    i := i + 1;
end loop;

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