from math import * from black_box import alldivs sums = [] tobe = [] a = range(1,10001) for i in a: summ = sum(alldivs(i)) if summ < 10000 and sum(alldivs(summ)) == i: sums.append([i, summ]) if i!= summ: tobe.append(i) answer = sum(tobe) print(sums) print(answer)
#What is the value of the first triangle number to have over five hundred divisors?
from black_box import alldivs
from black_box import numdivs
done = False
thisTri = 1
increment = 1
divListSizeMax = 0
while not done:
allDivs = []
divListSize = 0
increment += 1
thisTri += increment
divList = alldivs(thisTri)
divListSize = len(divList)
if(divListSize >= divListSizeMax):
divListSizeMax = divListSize
print("--")
print(increment)
print(thisTri)
print(divListSizeMax)
if(divListSize >= 500):
done = True
print(increment)
print(thisTri)
print(divListSize)
#Find the sum of all the positive integers which cannot be written as the sum
#of two abundant numbers.
from math import *
from black_box import alldivs
upperLimit = 28123
abundants = []
#find all the abundant numbers up to the upperlimit
for i in range(upperLimit):
if(i%1000 == 0):
print('{0:.2f}'.format(100 * i / upperLimit))
allTheseDivs = []
allTheseDivs = alldivs(i)
thisSum = sum(allTheseDivs[0:-1])
if(thisSum > i):
abundants.append(i)
print(abundants[0])
#SAVING TO FILE _______________________________________
file = open("../Reference/abundants.txt", "w")
for num in abundants:
file.write(str(num) + " ")
file.close()
#___________________________________
def commonFactors(newNumber, currentFactors):
newFact = alldivs(newNumber)
intersection = list(set(currentFactors) & set(newFact))
return intersection
#recursive function
def fourPrimeFacts(mainNumber, numSoFar, factors):
for num in factors:
newMain = mainNumber / num
commonFact = commonFactors(newMain, factors)
found = False
num = 1
while not found:
factors = alldivs(num)
if(len(factors) >= 4):
primeFactors = []
for fact in factors:
if(isprime(fact)):
primeFactors.append(fact)
#have list of all prime factors
if(len(primeFactors) >=4):
#At this point, I need to see if any combination
#of 4 of these will result in our num
#if i divide by one of them, and the result still has at least three of the others as factors, I can keep going
# The prime factors of 13195 are 5, 7, 13 and 29.
# What is the largest prime factor of the number 600851475143 ?
from black_box import isprime
from black_box import alldivs
divList = alldivs(600851475143)
answer = divList[-1]
for num in reversed(divList):
if(isprime(num)):
answer = num
break
print(answer)
