How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the BASIC programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the BASIC programming language
Table of Contents
Problem Statement
These define three classifications of positive integers based on their proper divisors. Let P(n) be the sum of the proper divisors of n where the proper divisors are all positive divisors of n other than n itself.
6 has proper divisors of 1, 2, and 3. 1 + 2 + 3 = 6, so 6 is classed as a perfect number.
Calculate how many of the integers 1 to 20,000 (inclusive) are in each of the three classes. Show the results here.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Abundant, deficient and perfect number classifications step by step in the BASIC programming language
Source code in the basic programming language
10 DEFINT A-Z: LM=20000
20 DIM P(LM)
30 FOR I=1 TO LM: P(I)=-32767: NEXT
40 FOR I=1 TO LM/2: FOR J=I+I TO LM STEP I: P(J)=P(J)+I: NEXT: NEXT
50 FOR I=1 TO LM
60 X=I-32767
70 IF P(I)<X THEN D=D+1 ELSE IF P(I)=X THEN P=P+1 ELSE A=A+1
80 NEXT
90 PRINT "DEFICIENT:";D
100 PRINT "PERFECT:";P
110 PRINT "ABUNDANT:";A
deficient = 0
perfect = 0
abundant = 0
for n = 1 to 20000
sum = SumProperDivisors(n)
begin case
case sum < n
deficient += 1
case sum = n
perfect += 1
else
abundant += 1
end case
next
print "The classification of the numbers from 1 to 20,000 is as follows :"
print
print "Deficient = "; deficient
print "Perfect = "; perfect
print "Abundant = "; abundant
end
function SumProperDivisors(number)
if number < 2 then return 0
sum = 0
for i = 1 to number \ 2
if number mod i = 0 then sum += i
next i
return sum
end function
100 cls
110 defic = 0
120 perfe = 0
130 abund = 0
140 for n = 1 to 20000
150 sump = SumProperDivisors(n)
160 if sump < n then
170 defic = defic+1
180 else
190 if sump = n then
200 perfe = perfe+1
210 else
220 if sump > n then abund = abund+1
230 endif
240 endif
250 next
260 print "The classification of the numbers from 1 to 20,000 is as follows :"
270 print
280 print "Deficient = ";defic
290 print "Perfect = ";perfe
300 print "Abundant = ";abund
310 end
320 function SumProperDivisors(number)
330 if number < 2 then SumProperDivisors = 0
340 sum = 0
350 for i = 1 to number/2
360 if number mod i = 0 then sum = sum+i
370 next i
380 SumProperDivisors = sum
390 end function
Public Sub Main()
Dim sum As Integer, deficient As Integer, perfect As Integer, abundant As Integer
For n As Integer = 1 To 20000
sum = SumProperDivisors(n)
If sum < n Then
deficient += 1
Else If sum = n Then
perfect += 1
Else
abundant += 1
Endif
Next
Print "The classification of the numbers from 1 to 20,000 is as follows : \n"
Print "Deficient = "; deficient
Print "Perfect = "; perfect
Print "Abundant = "; abundant
End
Function SumProperDivisors(number As Integer) As Integer
If number < 2 Then Return 0
Dim sum As Integer = 0
For i As Integer = 1 To number \ 2
If number Mod i = 0 Then sum += i
Next
Return sum
End Function
function sumProperDivisors(num)
if num > 1 then
sum = 1
root = sqr(num)
for i = 2 to root
if num mod i = 0 then
sum = sum + i
if (i*i) <> num then sum = sum + num / i
end if
next i
end if
sumProperDivisors = sum
end function
deficient = 0
perfect = 0
abundant = 0
print "The classification of the numbers from 1 to 20,000 is as follows :"
for n = 1 to 20000
sump = sumProperDivisors(n)
if sump < n then
deficient = deficient +1
else
if sump = n then
perfect = perfect +1
else
if sump > n then abundant = abundant +1
end if
end if
next n
print "Deficient = "; deficient
print "Perfect = "; perfect
print "Abundant = "; abundant
LET lm = 20000
DIM s(0)
MAT REDIM s(lm)
FOR i = 1 TO lm
LET s(i) = -32767
NEXT i
FOR i = 1 TO lm/2
FOR j = i+i TO lm STEP i
LET s(j) = s(j) +i
NEXT j
NEXT i
FOR i = 1 TO lm
LET x = i - 32767
IF s(i) < x THEN
LET d = d +1
ELSE
IF s(i) = x THEN
LET p = p +1
ELSE
LET a = a +1
END IF
END IF
NEXT i
PRINT "The classification of the numbers from 1 to 20,000 is as follows :"
PRINT
PRINT "Deficient ="; d
PRINT "Perfect ="; p
PRINT "Abundant ="; a
END
You may also check:How to resolve the algorithm XML/Input step by step in the PureBasic programming language
You may also check:How to resolve the algorithm Averages/Arithmetic mean step by step in the Red programming language
You may also check:How to resolve the algorithm Two bullet roulette step by step in the Go programming language
You may also check:How to resolve the algorithm Bioinformatics/base count step by step in the Forth programming language
You may also check:How to resolve the algorithm Ludic numbers step by step in the AppleScript programming language