401408000 has 204 divisors, whose sum is σ = 1165483332. Its totient is φ = 137625600.

The previous prime is 401407957. The next prime is 401408009. The reversal of 401408000 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 2 ways, for example, as 12845056 + 388562944 = 3584^2 + 19712^2 .

It is a super-2 number, since 2×401408000² = 322256764928000000, which contains 22 as substring.

It is a self number, because there is not a number n which added to its sum of digits gives 401408000.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (401408009) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 57343997 + ... + 57344003.

Almost surely, 2^401408000 is an apocalyptic number.

401408000 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 401408000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (582741666).

401408000 is an abundant number, since it is smaller than the sum of its proper divisors (764075332).

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

401408000 is an frugal number, since it uses more digits than its factorization.

401408000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 61 (or 14 counting only the distinct ones).

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

The square root of 401408000 is about 20035.1690783981. The cubic root of 401408000 is about 737.6698067294.

The spelling of 401408000 in words is "four hundred one million, four hundred eight thousand".