409001600 has 288 divisors, whose sum is σ = 1255946400. Its totient is φ = 128563200.

The previous prime is 409001531. The next prime is 409001603. The reversal of 409001600 is 6100904.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is not an unprimeable number, because it can be changed into a prime (409001603) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 13193585 + ... + 13193615.

It is an arithmetic number, because the mean of its divisors is an integer number (4360925).

Almost surely, 2^409001600 is an apocalyptic number.

409001600 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 409001600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (627973200).

409001600 is an abundant number, since it is smaller than the sum of its proper divisors (846944800).

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

409001600 is a wasteful number, since it uses less digits than its factorization.

409001600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 112 (or 64 counting only the distinct ones).

The product of its (nonzero) digits is 216, while the sum is 20.

The square root of 409001600 is about 20223.7879735721. The cubic root of 409001600 is about 742.2923799855.

The spelling of 409001600 in words is "four hundred nine million, one thousand, six hundred".