from tools import number_theory

def range_n(N):
    return int(((4 * N + 1) ** 0.5 - 3) / 4) + 1

def range_k(N, n):
    return int(((2 * N + n ** 2) ** 0.5 - 3 * n) / 2) + 1

def search(limit):
    count = 0
    for n in range(1, range_n(limit)):
        for k in range(1, range_k(limit, n), 2):
            if number_theory.gcd(n, k) > 1:
                continue
            p = 2 * n ** 2
            q = k ** 2
            r = 2 * n * k
            if (p + q + r) % abs(p - q):
                continue
            print(n, k)
            count += limit // (2 * p + 2 * q + 3 * r)
    return count

def perfect(limit):
    def side(n, k):
        return 4 * n ** 2 + 6 * n * k + 2 * k ** 2
    def sqrt2(n):
        m = int(n * 2 ** 0.5)
        return m + (1 - m % 2)
    n, k = 1, 1
    border = 12
    count = 0
    while border < limit:
        yield limit // border
        n = n + k
        k = sqrt2(n)
        border = side(n, k)

#print(search(100000000))
print(sum(list(perfect(100000000))))