413305200 has 720 divisors, whose sum is σ = 1893093120. Its totient is φ = 84672000.

The previous prime is 413305199. The next prime is 413305201. The reversal of 413305200 is 2503314.

It is an interprime number because it is at equal distance from previous prime (413305199) and next prime (413305201).

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413305201) 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 143 ways as a sum of consecutive naturals, for example, 5821165 + ... + 5821235.

It is an arithmetic number, because the mean of its divisors is an integer number (2629296).

Almost surely, 2^413305200 is an apocalyptic number.

413305200 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 413305200, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (946546560).

413305200 is an abundant number, since it is smaller than the sum of its proper divisors (1479787920).

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

413305200 is a wasteful number, since it uses less digits than its factorization.

413305200 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 123 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 360, while the sum is 18.

The square root of 413305200 is about 20329.9090012720. The cubic root of 413305200 is about 744.8868197358.

Adding to 413305200 its reverse (2503314), we get a palindrome (415808514).

The spelling of 413305200 in words is "four hundred thirteen million, three hundred five thousand, two hundred".