413481600 has 432 divisors, whose sum is σ = 1722135870. Its totient is φ = 94187520.

The previous prime is 413481583. The next prime is 413481631. The reversal of 413481600 is 6184314.

413481600 is a `hidden beast` number, since 4 + 13 + 48 + 1 + 600 = 666.

It can be written as a sum of positive squares in 3 ways, for example, as 386358336 + 27123264 = 19656^2 + 5208^2 .

It is an unprimeable number.

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 53 ways as a sum of consecutive naturals, for example, 1411054 + ... + 1411346.

Almost surely, 2^413481600 is an apocalyptic number.

413481600 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 413481600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (861067935).

413481600 is an abundant number, since it is smaller than the sum of its proper divisors (1308654270).

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

413481600 is a wasteful number, since it uses less digits than its factorization.

413481600 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 337 (or 310 counting only the distinct ones).

The product of its (nonzero) digits is 2304, while the sum is 27.

The square root of 413481600 is about 20334.2469740091. The cubic root of 413481600 is about 744.9927780331.

The spelling of 413481600 in words is "four hundred thirteen million, four hundred eighty-one thousand, six hundred".