How to resolve the algorithm Amicable pairs step by step in the uBasic/4tH programming language

Published on 12 May 2024 09:40 PM
#Ubasic/4th

How to resolve the algorithm Amicable pairs step by step in the uBasic/4tH 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 uBasic/4tH programming language

Source code in the ubasic/4th programming language

Input "Limit: ";l
Print "Amicable pairs < ";l

For n = 1 To l
  m = FUNC(_SumDivisors (n))-n
  If m = 0 Then Continue               ' No division by zero, please
  p = FUNC(_SumDivisors (m))-m
  If (n=p) * (n
Next

End

_LeastPower Param(2)
  Local(1)

  c@ = a@
  Do While (b@ % c@) = 0
    c@ = c@ * a@
  Loop

Return (c@)


' Return the sum of the proper divisors of a@

_SumDivisors Param(1)
  Local(4)

  b@ = a@
  c@ = 1

  ' Handle two specially

  d@ = FUNC(_LeastPower (2,b@))
  c@ = c@ * (d@ - 1)
  b@ = b@ / (d@ / 2)

  ' Handle odd factors

  For e@ = 3 Step 2 While (e@*e@) < (b@+1)
    d@ = FUNC(_LeastPower (e@,b@))
    c@ = c@ * ((d@ - 1) / (e@ - 1))
    b@ = b@ / (d@ / e@)
  Loop

  ' At this point, t must be one or prime

  If (b@ > 1) c@ = c@ * (b@+1)
Return (c@)

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