413013120 has 128 divisors (see below), whose sum is σ = 1417832640. Its totient is φ = 101658624.

The previous prime is 413013109. The next prime is 413013121. The reversal of 413013120 is 21310314.

It is a tau number, because it is divible by the number of its divisors (128).

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a self number, because there is not a number n which added to its sum of digits gives 413013120.

It is not an unprimeable number, because it can be changed into a prime (413013121) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 16687 + ... + 33233.

Almost surely, 2^413013120 is an apocalyptic number.

413013120 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 413013120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (708916320).

413013120 is an abundant number, since it is smaller than the sum of its proper divisors (1004819520).

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

413013120 is a wasteful number, since it uses less digits than its factorization.

413013120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 16582 (or 16570 counting only the distinct ones).

The product of its (nonzero) digits is 72, while the sum is 15.

The square root of 413013120 is about 20322.7242268353. The cubic root of 413013120 is about 744.7113095532.

Adding to 413013120 its reverse (21310314), we get a palindrome (434323434).

The spelling of 413013120 in words is "four hundred thirteen million, thirteen thousand, one hundred twenty".