414000409 has 3 divisors (see below), whose sum is σ = 414020757. Its totient is φ = 413980062.

The previous prime is 414000359. The next prime is 414000449. The reversal of 414000409 is 904000414.

It is a happy number.

The square root of 414000409 is 20347.

It is a perfect power (a square), and thus also a powerful number.

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length.

It is not a de Polignac number, because 414000409 - 2⁹ = 413999897 is a prime.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 414000409.

It is not an unprimeable number, because it can be changed into a prime (414000449) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 10174 + ... + 30520.

It is an arithmetic number, because the mean of its divisors is an integer number (138006919).

Almost surely, 2^414000409 is an apocalyptic number.

414000409 is the 20347-th square number.

414000409 is the 10174-th centered octagonal number.

It is an amenable number.

414000409 is a deficient number, since it is larger than the sum of its proper divisors (20348).

414000409 is an frugal number, since it uses more digits than its factorization.

414000409 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40694 (or 20347 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The cubic root of 414000409 is about 745.3042368062.

Multiplying 414000409 by its product of nonzero digits (576), we get a square (238464235584 = 488328²).

The spelling of 414000409 in words is "four hundred fourteen million, four hundred nine", and thus it is an aban number.