sigma5.py

@numba.jit("i4(i4, i4)", nopython=True, nogil=True)
def gcd(a, b):
    while True:
        if a == 0: return b
        if b == 0: return a
        if a == b: return a
        if b > a: 
            a, b = a, b % a
        else:
            a, b = a % b, b
            
@numba.jit("f8(i4)", nopython=True, nogil=True)
def f(n):
    arr = np.zeros(n, dtype=np.float64)
    for i in np.arange(1, n + 1):
        arr[i - 1] = np.log(gcd(i, n))
    return np.exp(np.sum(arr) / n)

@numba.jit("i4[:](i4)", nopython=True, nogil=True)
def g(N):
    result = np.zeros(N, dtype=np.int32)
    n = 1
    i = 0
    fm = -np.inf
    while i < N:
        f0 = f(n)
        if f0 > fm:
            result[i] = n
            i += 1
            fm = f0
        n += 1
    return result