413085312 has 256 divisors, whose sum is σ = 1321920000. Its totient is φ = 126517248.

The previous prime is 413085307. The next prime is 413085331. The reversal of 413085312 is 213580314.

It is a happy number.

413085312 is a `hidden beast` number, since 41 + 308 + 5 + 312 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

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 31 ways as a sum of consecutive naturals, for example, 4641364 + ... + 4641452.

It is an arithmetic number, because the mean of its divisors is an integer number (5163750).

Almost surely, 2^413085312 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413085312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (660960000).

413085312 is an abundant number, since it is smaller than the sum of its proper divisors (908834688).

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

413085312 is a wasteful number, since it uses less digits than its factorization.

413085312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 208 (or 190 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 27.

The square root of 413085312 is about 20324.5002890600. The cubic root of 413085312 is about 744.7546972522.

The spelling of 413085312 in words is "four hundred thirteen million, eighty-five thousand, three hundred twelve".