25

from math import gcd


def divs(n, s='find'):
    d = set()
    for i in range(1, int((n ** (1 / 2))) + 1):
        if n % i == 0:
            d.add(i)
            d.add(n // i)
    d = list(d)
    d.sort()
    l = len(d)
    if s == 'count':
        return l
    if s == 'find':
        return d
    return "s может быть только 'find' или 'count'"


def is_palindrome(n):
    n = str(n)
    return n == n[::-1]


def p1():
    for x in range(300000, 333001):
        if divs(x, 'count') == 3:
            print(x)


def p2():
    for x in range(88535, 153374):
        k = divs(x)
        if [y % 2 == 1 for y in k].count(1) == 5:
            print(x)


def p3():
    for x in range(198374, 295382):
        k = divs(x)
        if [y % 2 == 1 for y in k].count(1) == 7:
            k.reverse()
            for y in k:
                if y % 2 == 1:
                    print(y)


def p4():
    l = 0
    for x in range(100100, 300301):
        if divs(x, 'count') - 2 == 3:
            l += 1
    print(l)


def p5():
    k = 0
    max = -1
    for x in range(231893, 251860):
        l = divs(x, 'count')
        if l >= k:
            max = x
            k = l

    print(k, max)


def p6():
    k = 0
    for x in range(55556, 55777):
        if divs(x, 'count') == 2:
            k += 1
    print(k)


def p7(n):
    return divs(n, 'count')


def p8():
    k = 0
    max = 0
    for x in range(100, 100101):
        if divs(x, 'count') == 2:
            k += 1
            max = x
    print(k, max)


def p9():
    k = 0
    min = -1
    for x in range(591645, 592846):
        l = divs(x, 'count')
        if l > k:
            min = x
            k = l

    print(min)


def p10():
    k = 0
    for x in range(12345, 12426):
        l = divs(x)
        if any(is_palindrome(x) for x in l if x > 9):
            k += 1
    print(k)


def p11():
    k = 0
    for x in range(300000, 333001):
        if divs(x, 'count') == 3:
            k += 1
    print(k)


def p12():
    k = 0
    for x in range(53671, 125699):
        if divs(x, 'count') == 5:
            k += 1
    print(k)


def p13(n):
    k = 0
    for x in range(1, n):
        if gcd(x, n) == 1:
            k += 1
    return k


def p14():
    k = 0
    for x in divs(9999556):
        k += p13(x)
    print(k)


def p15():
    m = p13(1013)
    a = [x for x in range(0, 1014) if gcd(x, 1013) == 1]
    summ = 0
    for x in a:
        summ += (x ** (m)) % 1013
    print(summ / len(a))


def p16():
    a = divs(230010)
    b = divs(600270)
    c = [x for x in a if x in b]
    print(c)


def p17():
    k = 0
    for x in range(1, 10001):
        if [x % 2 == 1 for x in divs(x)].count(1) == 1:
            k += 1
    print(k)


def M(n):
    d = divs(n)
    l = len(d)
    if l < 6:
        return 0
    else:
        return d[1] * d[2] * d[3] * d[4] * d[5]


def p18():
    k = 0
    for x in range(500000000, 520000000):
        if 0 < M(x) < x:
            print(f'{x}. {M(x)}')
            k += 1
            if k == 5:
                break


def p19():
    for y in range(190201, 190281):
        m = divs(y)
        if [x % 2 == 0 for x in m].count(1) == 4:
            for x in range(len(m) - 1, 0, -1):
                if m[x] % 2 == 0:
                    print(m[x], end=' ')
            print('\n')


def M1(n):
    d = divs(n)  # включая 1 и n
    l = len(d)
    d.pop(0)
    d.pop(-1)
    if l <= 3:
        return 0
    else:
        return max(d) + min(d)


def p20():
    k = 0
    for x in range(452022, 502021):
        if M1(x) % 7 == 3:
            print(x, M1(x))
            k += 1
            if k == 5:
                break


def p21():
    k = 0
    for x in range(88535, 153374):
        if [x % 2 == 1 for x in divs(x)].count(1) == 5:
            k += 1
    print(k)


def p22():
    k = 0
    for x in range(88535, 153374):
        if [x % 2 == 0 for x in divs(x)].count(1) == 5:
            k += 1
    print(k)


def p23():
    for y in range(198374, 295382):
        m = divs(y)
        if [x % 2 == 1 for x in m].count(1) == 7:
            for x in range(len(m) - 1, -1, -1):
                if m[x] % 2 == 1:
                    print(m[x], end=' ')
            print('\n')


def p24():
    k = 0
    for y in range(100100, 300301):
        if len([x for x in divs(y)]) == 5:
            k += 1
    print(k)


def p25():
    k = 0
    for y in range(52112, 623123):
        if len([x for x in divs(y) if divs(x, 'count') == 2]) == 3:
            k += 1
    print(k)


def p26():
    k = 0
    a = [x for x in range(1000)]
    for x in range(2, len(a)):
        for y in range(x ** 2, len(a), x):
            a[y] = 0
    a.sort()
    a = set(a)
    a.remove(0)
    a.remove(1)
    b = [x ** 2 for x in a]
    for x in range(52112, 623122):
        if len([y for y in divs(x) if y in b]) == 3:
            k += 1
    print(k)


def p27():
    k = 0
    s = 0
    for y in range(88535, 167043):
        m = divs(y)
        if [x % 2 == 0 for x in m].count(1) == 5:
            k += 1
            s += y
    print(k, (s / k))


def p28():
    d = set()
    for m in range(0, 100):
        for n in range(0, 100):
            if len(str(int((4 ** (m)) * (5 ** n)))) == 9:
                d.add((4 ** (m)) * (5 ** n))
    d = list(d)
    d.sort()
    k = 0
    for x in range(200000000, 600000001):
        if x in d:
            k += 1
    print(k)


def p29():
    k = 0
    d = set()
    for m in range(0, 1000, 2):
        for n in range(1, 1000, 2):
            if 200000000 <= (2 ** m) * (3 ** n) <= 400000000:
                k += 1
    print(k)


def p30():
    k = 0
    for n in range(0, 1000, 2):
        for m in range(1, 1000, 2):
            if 100000000 <= (5 ** m) * (7 ** n) <= 600000000:
                k += 1
                print((5 ** n) * (7 ** m))