400800400 has 405 divisors, whose sum is σ = 1333217403. Its totient is φ = 115315200.

The previous prime is 400800373. The next prime is 400800403. The reversal of 400800400 is 4008004.

The square root of 400800400 is 20020.

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

It can be written as a sum of positive squares in 4 ways, for example, as 103306896 + 297493504 = 10164^2 + 17248^2 .

It is a Harshad number since it is a multiple of its sum of digits (16).

It is not an unprimeable number, because it can be changed into a prime (400800403) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 30830794 + ... + 30830806.

Almost surely, 2^400800400 is an apocalyptic number.

400800400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

400800400 is the 20020-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 400800400

400800400 is an abundant number, since it is smaller than the sum of its proper divisors (932417003).

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

400800400 is a wasteful number, since it uses less digits than its factorization.

400800400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 80 (or 38 counting only the distinct ones).

The product of its (nonzero) digits is 128, while the sum is 16.

The cubic root of 400800400 is about 737.2974220969.

Multiplying 400800400 by its sum of digits (16), we get a square (6412806400 = 80080²).

400800400 divided by its sum of digits (16) gives a square (25050025 = 5005²).

Adding to 400800400 its reverse (4008004), we get a palindrome (404808404).

400800400 divided by its reverse (4008004) gives a square (100 = 10²).

The spelling of 400800400 in words is "four hundred million, eight hundred thousand, four hundred".