401408 has 42 divisors (see below), whose sum is σ = 933831. Its totient is φ = 172032.

The previous prime is 401407. The next prime is 401411. The reversal of 401408 is 804104.

It is a happy number.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 200704 + 200704 = 448^2 + 448^2 .

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=448.

It is a super-2 number, since 2×401408² = 322256764928, which contains 22 as substring.

It is a Duffinian number.

It is a nialpdrome in base 14 and base 16.

It is not an unprimeable number, because it can be changed into a prime (401407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 57341 + ... + 57347.

2⁴⁰¹⁴⁰⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 401408

401408 is an abundant number, since it is smaller than the sum of its proper divisors (532423).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

401408 is an frugal number, since it uses more digits than its factorization.

401408 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 40 (or 9 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 17.

The square root of 401408 is about 633.5676759431. The cubic root of 401408 is about 73.7669806729.

Multiplying 401408 by its product of nonzero digits (128), we get a square (51380224 = 7168²).

401408 divided by its product of nonzero digits (128) gives a square (3136 = 56²).

The spelling of 401408 in words is "four hundred one thousand, four hundred eight".