401456210400 has 1728 divisors, whose sum is σ = 1800514759680. Its totient is φ = 82059264000.

The previous prime is 401456210329. The next prime is 401456210401. The reversal of 401456210400 is 4012654104.

401456210400 is a `hidden beast` number, since 4 + 0 + 1 + 45 + 6 + 210 + 400 = 666.

It is a super-2 number, since 2×401456210400² (a number of 24 digits) contains 22 as substring.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (401456210401) by changing a digit.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 2658650325 + ... + 2658650475.

It is an arithmetic number, because the mean of its divisors is an integer number (1041964560).

Almost surely, 2^401456210400 is an apocalyptic number.

401456210400 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 401456210400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (900257379840).

401456210400 is an abundant number, since it is smaller than the sum of its proper divisors (1399058549280).

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

401456210400 is a wasteful number, since it uses less digits than its factorization.

401456210400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 337 (or 321 counting only the distinct ones).

The product of its (nonzero) digits is 3840, while the sum is 27.

Adding to 401456210400 its reverse (4012654104), we get a palindrome (405468864504).

The spelling of 401456210400 in words is "four hundred one billion, four hundred fifty-six million, two hundred ten thousand, four hundred".