401824 has 24 divisors (see below), whose sum is σ = 820260. Its totient is φ = 193536.

The previous prime is 401813. The next prime is 401827. The reversal of 401824 is 428104.

401824 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 2 ways, for example, as 384400 + 17424 = 620^2 + 132^2 .

It is a super-2 number, since 2×401824² = 322925053952, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (401827) by changing a digit.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 712 + ... + 1144.

2⁴⁰¹⁸²⁴ 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 401824, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (410130).

401824 is an abundant number, since it is smaller than the sum of its proper divisors (418436).

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

401824 is a wasteful number, since it uses less digits than its factorization.

401824 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 472 (or 464 counting only the distinct ones).

The product of its (nonzero) digits is 256, while the sum is 19.

The square root of 401824 is about 633.8958905057. The cubic root of 401824 is about 73.7924547286.

Adding to 401824 its reverse (428104), we get a palindrome (829928).

It can be divided in two parts, 40182 and 4, that added together give a triangular number (40186 = T₂₈₃).

The spelling of 401824 in words is "four hundred one thousand, eight hundred twenty-four".