Competitive-Helper

Various utilities to help with competitive programming/math. Including, solving recurrences,
from here: https://github.com/lion137/Linear_Recurrence_Solver.
Before starts, run prime sieve to 10 milions - to reasonably fast factorize numbers up to 10^16. No dependencies, just standard library.
Functions:

• is_prime;
• divisors(n) - all divisors of n;
• primes(n) - primes up to n;
• factorize(n) - factors of n;
• distinct_factors(n);
• totient(n) - Eulers Totient function;
• ndivisors(n) - number of divisors of n;
• sdivisors(n) - sum of proper divisors;
• lcm(n, m) - Least Common Multiple of n, m;
• recurrence(n, vec, vec1) - solves recurrence: https://github.com/lion137/Linear_Recurrence_Solver;
• recurrence_mod(n, vec, vec1, mod) - solves recurrence modulo;
• pow_mod(a, n, m) - power of a to n modulo m.
• reduce_series(op, f, start, end, e=None) - applies an op to the series f, from start to the end exclusive, read the docs for more.
  Ex: reduce_series(add, lambda x: 1 / n, 1, 5) = 2.083333333333333 - Harmonic series: https://en.wikipedia.org/wiki/Harmonic_series_(mathematics)

One can, also, rise a matrix to some power n >= 0 .
Any suggestions, bugs, comment here or on: https://lion137.blogspot.com/2018/12/competitive-math-helper.html
Could be use directly in code or as a quick check in console: