func legendre_phi(x, a) is cached {
    return x if (a <= 0)
    __FUNC__(x, a-1) - __FUNC__(idiv(x, a.prime), a-1)
}

func legendre_prime_count(n) is cached {
    return 0 if (n < 2)
    var a = __FUNC__(n.isqrt)
    legendre_phi(n, a) + a - 1
}

print("e             n   Legendre    builtin\n",
      "-             -   --------    -------\n")

for n in (1 .. 9) {
    printf("%d  %12d %10d %10d\n", n, 10**n,
        legendre_prime_count(10**n), prime_count(10**n))
    assert_eq(legendre_prime_count(10**n), prime_count(10**n))
}