409765120 has 72 divisors (see below), whose sum is σ = 990551016. Its totient is φ = 162398208.

The previous prime is 409765087. The next prime is 409765163. The reversal of 409765120 is 21567904.

It can be written as a sum of positive squares in 4 ways, for example, as 1401856 + 408363264 = 1184^2 + 20208^2 .

It is a super-2 number, since 2×409765120² = 335814907137228800, which contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 143224 + ... + 146056.

It is an arithmetic number, because the mean of its divisors is an integer number (13757653).

Almost surely, 2^409765120 is an apocalyptic number.

409765120 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 409765120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (495275508).

409765120 is an abundant number, since it is smaller than the sum of its proper divisors (580785896).

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

409765120 is a wasteful number, since it uses less digits than its factorization.

409765120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2967 (or 2953 counting only the distinct ones).

The product of its (nonzero) digits is 15120, while the sum is 34.

The square root of 409765120 is about 20242.6559522213. The cubic root of 409765120 is about 742.7539941311.

The spelling of 409765120 in words is "four hundred nine million, seven hundred sixty-five thousand, one hundred twenty".