<reponame>lcsm29/project-euler<filename>py/py_0722_slowly_converging_series.py
# Solution of;
# Project Euler Problem 722: Slowly converging series
# https://projecteuler.net/problem=722
# 
# For a non-negative integer $k$, define\[E_k(q) = \sum\limits_{n = 1}^\infty 
# \sigma_k(n)q^n\]where $\sigma_k(n) = \sum_{d \mid n} d^k$ is the sum of the 
# $k$-th powers of the positive divisors of $n$. It can be shown that, for 
# every $k$, the series $E_k(q)$ converges for any $0 < q < 1$. For 
# example,$E_1(1 - \frac{1}{2^4}) = \mathrm{3. 872155809243e2}$$E_3(1 - 
# \frac{1}{2^8}) = \mathrm{2. 767385314772e10}$$E_7(1 - \frac{1}{2^{15}}) = 
# \mathrm{6. 725803486744e39}$All the above values are given in scientific 
# notation rounded to twelve digits after the decimal point. Find the value of 
# $E_{15}(1 - \frac{1}{2^{25}})$. Give the answer in scientific notation 
# rounded to twelve digits after the decimal point.
# 
# by lcsm29 http://github.com/lcsm29/project-euler
import timed


def dummy(n):
    pass


if __name__ == '__main__':
    n = 1000
    i = 10000
    prob_id = 722
    timed.caller(dummy, n, i, prob_id)
