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from functools import reduce
from itertools import count
def sum_digits(n):
return reduce(lambda x, y: x + int(y), str(n), 0)
def triangular(n):
return n * (n+1) // 2
def pentagonal(n):
return n * (3*n - 1) // 2
def hexagonal(n):
return n * (2*n - 1)
def is_triangular(n):
for i in count(1):
t = triangular(i)
if t >= n:
return t == n
# def is_pentagonal(n):
# for i in count(1):
# p = pentagonal(i)
# if p >= n:
# return p == n
# def is_hexagonal(n):
# for i in count(1):
# h = hexagonal(i)
# if h >= n:
# return h == n
def proper_divisors(num):
divisor = []
for i in range(1, num):
if num % i == 0:
divisor.append(i)
return divisor
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