Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
cevap : 31626
ipucu icin buraya bakabilirsiniz.
Derleme ortami pycharm python
main.py dosyasi:
import func
checked_list = []
for number in range (2,10001):
sum = func.all_calculations(number)
number2 = sum
sum2 = func.all_calculations(number2)
if (number == sum2) & (number != sum):
checked_list.append(number)
result_sum = 0
for i in range(len(checked_list)):
result_sum += checked_list[i]
print("##########################")
print("hesaplamalar tamam")
print("1-10000 arasindaki amicable sayilarin listesi : ", checked_list)
print("amicable sayilarin toplami : ", result_sum)
func.py dosyasi :
import collections # OrderedDict icin library - eleman_sayilarini_iliskilendir fonk'unun icinde
def prime_divisor_calc(number):
i = 2
list = []
while (i <= number):
if (number % i) == 0:
division = number / i
number = division
list.append(i)
else:
i = i + 1
return list
def number_of_list_items(list):
list_items = []
for i, item in enumerate(list):
list_items.append(list.count(item))
return list_items
def correlate_item_numbers(list_1, list_2):
dict = collections.OrderedDict()
for i in range(len(list_1)):
dict[list_1[i]] = list_2[i]
return dict
def sum_of_divisors(dict,number):
product = 1
for i in range(len(dict)):
product = product * (pow(list(dict.keys())[i], list(dict.values())[i] + 1) - 1) / (list(dict.keys())[i] - 1)
sum = product - number #project euler soru 21'de toplamda sayinin kendisinin dahil edilmesini istemiyor.
return sum
def all_calculations(number):
divisors_list = prime_divisor_calc(number)
print("bolenler listesi:", divisors_list)
list_items = number_of_list_items(divisors_list)
dict = correlate_item_numbers(divisors_list, list_items)
# hangi carpandan kac tane var ekrana bas
for i in range(len(dict)):
print("%s den %s tane var" % (list(dict.keys())[i], list(dict.values())[i]))
sum = sum_of_divisors(dict, number)
return sum