401385600 has 576 divisors, whose sum is σ = 1795510080. Its totient is φ = 82944000.

The previous prime is 401385563. The next prime is 401385601. The reversal of 401385600 is 6583104.

401385600 is a `hidden beast` number, since 40 + 13 + 8 + 5 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (576).

It is a super-2 number, since 2×401385600² = 322220799774720000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (401385601) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 2217510 + ... + 2217690.

It is an arithmetic number, because the mean of its divisors is an integer number (3117205).

Almost surely, 2^401385600 is an apocalyptic number.

401385600 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 401385600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (897755040).

401385600 is an abundant number, since it is smaller than the sum of its proper divisors (1394124480).

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

401385600 is a wasteful number, since it uses less digits than its factorization.

401385600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 229 (or 209 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 401385600 is about 20034.6100536047. The cubic root of 401385600 is about 737.6560849375.

The spelling of 401385600 in words is "four hundred one million, three hundred eighty-five thousand, six hundred".