401616400 has 60 divisors (see below), whose sum is σ = 974534724. Its totient is φ = 159040000.

The previous prime is 401616373. The next prime is 401616401. The reversal of 401616400 is 4616104.

It can be written as a sum of positive squares in 6 ways, for example, as 21678336 + 379938064 = 4656^2 + 19492^2 .

It is a super-2 number, since 2×401616400² = 322591465497920000, which contains 22 as substring.

It is not an unprimeable number, because it can be changed into a prime (401616401) 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 11 ways as a sum of consecutive naturals, for example, 35430 + ... + 45370.

Almost surely, 2^401616400 is an apocalyptic number.

401616400 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 401616400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (487267362).

401616400 is an abundant number, since it is smaller than the sum of its proper divisors (572918324).

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

401616400 is a wasteful number, since it uses less digits than its factorization.

401616400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10060 (or 10049 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

The square root of 401616400 is about 20040.3692580751. The cubic root of 401616400 is about 737.7974439390.

The spelling of 401616400 in words is "four hundred one million, six hundred sixteen thousand, four hundred".