How to resolve the algorithm Numbers which are the cube roots of the product of their proper divisors step by step in the ALGOL 68 programming language

Published on 12 May 2024 09:40 PM
#Algol 68

How to resolve the algorithm Numbers which are the cube roots of the product of their proper divisors step by step in the ALGOL 68 programming language

Table of Contents

Problem Statement

Consider the number 24. Its proper divisors are: 1, 2, 3, 4, 6, 8 and 12. Their product is 13,824 and the cube root of this is 24. So 24 satisfies the definition in the task title. Compute and show here the first 50 positive integers which are the cube roots of the product of their proper divisors. Also show the 500th and 5,000th such numbers. Compute and show the 50,000th such number. OEIS considers 1 to be the first number in this sequence even though, strictly speaking, it has no proper divisors. Please therefore do likewise.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Numbers which are the cube roots of the product of their proper divisors step by step in the ALGOL 68 programming language

Source code in the algol programming language

BEGIN # find some numbers which are the cube roots of the product of their   #
      #      proper divisors                                                 #
      # the Online Encyclopedia of Integer Sequences states that these       #
      # numbers are 1 and those with eight divisors                          #
      # NB: numbers with 8 divisors have 7 proper divisors                   #
    INT max number = 500 000; # maximum number we will consider              #
    # form a table of proper divisor counts - assume the pdc of 1 is 7       #
    [ 1 : max number ]INT pdc; FOR i TO UPB pdc DO pdc[ i ] := 1 OD;
    pdc[ 1 ] := 7;
    FOR i FROM 2 TO UPB pdc DO
        FOR j FROM i + i BY i TO UPB pdc DO pdc[ j ] +:= 1 OD
    OD;
    # show the numbers which are the cube root of their proper divisor       #
    # product - equivalent to finding the numbers with a proper divisor      #
    # count of 7 ( we have "cheated" and set the pdc of 1 to 7 )             # 
    INT next show := 500;
    INT c count   := 0;
    FOR n TO UPB pdc DO
        IF pdc[ n ] = 7 THEN
            # found a suitable number                                        #
            IF ( c count +:= 1 ) <= 50 THEN
                print( ( " ", whole( n, -3 ) ) );
                IF c count MOD 10 = 0 THEN print( ( newline ) ) FI
            ELIF c count = next show THEN
                print( ( whole( c count, -9 ), "th: ", whole( n, 0 ), newline ) );
                next show *:= 10
            FI
        FI
    OD
END

You may also check:How to resolve the algorithm 100 prisoners step by step in the Raku programming language
You may also check:How to resolve the algorithm Write language name in 3D ASCII step by step in the Dart programming language
You may also check:How to resolve the algorithm Nth root step by step in the J programming language
You may also check:How to resolve the algorithm RIPEMD-160 step by step in the Kotlin programming language
You may also check:How to resolve the algorithm Loops/N plus one half step by step in the Action! programming language