413530400 has 108 divisors (see below), whose sum is σ = 1034101782. Its totient is φ = 161464320.

The previous prime is 413530399. The next prime is 413530543. The reversal of 413530400 is 4035314.

It can be written as a sum of positive squares in 9 ways, for example, as 34527376 + 379003024 = 5876^2 + 19468^2 .

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

It is a congruent number.

It is an unprimeable number.

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 17 ways as a sum of consecutive naturals, for example, 4263152 + ... + 4263248.

Almost surely, 2^413530400 is an apocalyptic number.

413530400 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 413530400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (517050891).

413530400 is an abundant number, since it is smaller than the sum of its proper divisors (620571382).

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

413530400 is an equidigital number, since it uses as much as digits as its factorization.

413530400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 263 (or 177 counting only the distinct ones).

The product of its (nonzero) digits is 720, while the sum is 20.

The square root of 413530400 is about 20335.4468846888. The cubic root of 413530400 is about 745.0220854375.

Adding to 413530400 its reverse (4035314), we get a palindrome (417565714).

The spelling of 413530400 in words is "four hundred thirteen million, five hundred thirty thousand, four hundred".