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# Detecting Smith numbers

After learning about Smith numbers today I cooked up this script fairly quickly. There are many places where it could be optimized and cleaned up but that wasn’t really the point – I just needed something that was accurate, and I’m pretty sure this is.

It also helped me to learn about the ulimit command after running it with a HUGE number that had taken up about 7GB of swap before I had to kill the process remotely via SSH…

``````
#!/usr/bin/python
# smith number detector - TWS 1-12-13

def detectSmith(num):
if(sumFactors(num) == sumDigits(num)):
return True
else:
return False

# calculate the sum of the factors
def sumFactors(num):
factorList = factors(num)
sum = 0

for factor in factorList:
if factor > 9:
# if a number (base ten) has multiple digits it has to be broken down
sum = sum + sumDigits(factor)
else:
sum = sum + factor

return sum

# sum the digits in a number with two or more
def sumDigits(num):
sum = 0

if num > 9:
while num > 9:
sum = sum + num % 10
num = num / 10
sum = sum + num
return sum
else:
# should never reach this
return num

def factors(num):
primeFactorList = []

factor = lowestPrimeFactor(num)
currentNum = num

while factor != -1:
primeFactorList.append(factor)
currentNum = currentNum / factor
factor = lowestPrimeFactor(currentNum)

if(currentNum != num):
# preventing returning the number passed in
primeFactorList.append(currentNum)

return primeFactorList

def lowestPrimeFactor(num):
for x in range(2, (num / 2) + 1):
if(num % x == 0):
return x
return -1

for number in range(1, 1000):
if(detectSmith(number)):
print "The number", number, "is a Smith number."
``````