413221120 has 144 divisors (see below), whose sum is σ = 1122891840. Its totient is φ = 144433152.

The previous prime is 413221117. The next prime is 413221153. The reversal of 413221120 is 21122314.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a junction number, because it is equal to n+sod(n) for n = 413221094 and 413221103.

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 315507 + ... + 316813.

It is an arithmetic number, because the mean of its divisors is an integer number (7797860).

Almost surely, 2^413221120 is an apocalyptic number.

413221120 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 413221120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (561445920).

413221120 is an abundant number, since it is smaller than the sum of its proper divisors (709670720).

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

413221120 is a wasteful number, since it uses less digits than its factorization.

413221120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1360 (or 1346 counting only the distinct ones).

The product of its (nonzero) digits is 96, while the sum is 16.

The square root of 413221120 is about 20327.8410068556. The cubic root of 413221120 is about 744.8363047400.

Adding to 413221120 its reverse (21122314), we get a palindrome (434343434).

It can be divided in two parts, 4132 and 21120, that added together give a palindrome (25252).

The spelling of 413221120 in words is "four hundred thirteen million, two hundred twenty-one thousand, one hundred twenty".