400768 has 32 divisors (see below), whose sum is σ = 832320. Its totient is φ = 192000.

The previous prime is 400759. The next prime is 400823. The reversal of 400768 is 867004.

It is a tau number, because it is divible by the number of its divisors (32).

It is a super-2 number, since 2×400768² = 321229979648, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

400768 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 3918 + ... + 4018.

It is an arithmetic number, because the mean of its divisors is an integer number (26010).

2⁴⁰⁰⁷⁶⁸ 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 400768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (416160).

400768 is an abundant number, since it is smaller than the sum of its proper divisors (431552).

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

400768 is a wasteful number, since it uses less digits than its factorization.

400768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 146 (or 134 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 25.

The square root of 400768 is about 633.0623981884. The cubic root of 400768 is about 73.7277554286.

Subtracting from 400768 its product of nonzero digits (1344), we obtain a square (399424 = 632²).

The spelling of 400768 in words is "four hundred thousand, seven hundred sixty-eight".