413112960 has 320 divisors, whose sum is σ = 1591377480. Its totient is φ = 101523456.

The previous prime is 413112907. The next prime is 413112977. The reversal of 413112960 is 69211314.

It can be written as a sum of positive squares in 4 ways, for example, as 112021056 + 301091904 = 10584^2 + 17352^2 .

It is a tau number, because it is divible by the number of its divisors (320).

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 39 ways as a sum of consecutive naturals, for example, 673614 + ... + 674226.

Almost surely, 2^413112960 is an apocalyptic number.

413112960 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 413112960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (795688740).

413112960 is an abundant number, since it is smaller than the sum of its proper divisors (1178264520).

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

413112960 is a wasteful number, since it uses less digits than its factorization.

413112960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 657 (or 636 counting only the distinct ones).

The product of its (nonzero) digits is 1296, while the sum is 27.

The square root of 413112960 is about 20325.1804420035. The cubic root of 413112960 is about 744.7713124790.

The spelling of 413112960 in words is "four hundred thirteen million, one hundred twelve thousand, nine hundred sixty".