How to resolve the algorithm Arithmetic numbers step by step in the FutureBasic programming language

Published on 12 May 2024 09:40 PM
#Futurebasic

How to resolve the algorithm Arithmetic numbers step by step in the FutureBasic programming language

Table of Contents

Problem Statement

A positive integer n is an arithmetic number if the average of its positive divisors is also an integer. Clearly all odd primes p must be arithmetic numbers because their only divisors are 1 and p whose sum is even and hence their average must be an integer. However, the prime number 2 is not an arithmetic number because the average of its divisors is 1.5. 30 is an arithmetic number because its 7 divisors are: [1, 2, 3, 5, 6, 10, 15, 30], their sum is 72 and average 9 which is an integer. Calculate and show here:

  1. The first 100 arithmetic numbers.
  2. The xth arithmetic number where x = 1,000 and x = 10,000.
  3. How many of the first x arithmetic numbers are composite. Note that, technically, the arithmetic number 1 is neither prime nor composite. Carry out the same exercise in 2. and 3. above for x = 100,000 and x = 1,000,000.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Arithmetic numbers step by step in the FutureBasic programming language

Source code in the futurebasic programming language

' Rosetta Code problem: https://rosettacode.org/wiki/Arithmetic_numbers
' by Rich Love, 9/21/22
' FutureBasic 7.0.14

output file "Arithmetic numbers.app"
Dim As long N = 1, ArithCnt = 0, CompCnt = 0
Dim As long Div, DivCnt, Sum, Quot

toolbox Microseconds( UnsignedWide * microTickCount )
dim as UnsignedWide   Time1, Time2

window 1, @"Arithmetic numbers",(0,0,600,200)

Print "The first 100 arithmetic numbers are:"

Microseconds( @Time1 )  //start time

for N = 1 to 2000000)
  
  Div = 1 : DivCnt = 0 : Sum = 0
  
  while 1
    
    Quot = N / Div
    If Quot < Div Then Exit while
    If Quot = Div And (N Mod Div) = 0 'N is a square
      Sum += Quot
      DivCnt += 1
      Exit while
    End If
    If (N Mod Div) = 0
      Sum += Div + Quot
      DivCnt += 2
    End If
    Div ++
    
  wend
  
  
  
  If (Sum Mod DivCnt) = 0                   'N is arithmetic
    ArithCnt ++
    
    If ArithCnt <= 100
      Print Using "####"; N;
      If (ArithCnt Mod 20) = 0 Then PRINT
    End If
    
    If DivCnt > 2 Then CompCnt ++
    
    Select Case ArithCnt
      Case 1e3
        PRINT
        PRINT  USING "The #######th arithmetic number is";ArithCnt;
        PRINT  USING "#####,### up to which ";N;
        PRINT  USING "###,### are composite. ";compcnt
      Case 1e4, 1e5, 1e6
        PRINT  USING "The #######th arithmetic number is";ArithCnt;
        PRINT  USING "#####,### up to which ";N;
        PRINT  USING "###,### are composite. ";compcnt
    End Select
    
    if ArithCnt = 1e6 then exit next
  End If
  
  
next N

Microseconds( @Time2 )  //end time

float TimeTaken
TimeTaken = (Time2.lo-Time1.lo)/1000/100/10
print
print "It took " + str$(TimeTaken) + " seconds to complete." // Approx 1.2 seconds on a M1 Mac Mini ( Macmini9,1 )


handleevents

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