409959040 has 64 divisors (see below), whose sum is σ = 996219720. Its totient is φ = 161280000.

The previous prime is 409959031. The next prime is 409959089. The reversal of 409959040 is 40959904.

It can be written as a sum of positive squares in 4 ways, for example, as 169833024 + 240126016 = 13032^2 + 15496^2 .

It is a tau number, because it is divible by the number of its divisors (64).

It is a Harshad number since it is a multiple of its sum of digits (40).

It is a junction number, because it is equal to n+sod(n) for n = 409958984 and 409959002.

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, 33790 + ... + 44290.

Almost surely, 2^409959040 is an apocalyptic number.

409959040 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 409959040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (498109860).

409959040 is an abundant number, since it is smaller than the sum of its proper divisors (586260680).

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

409959040 is a wasteful number, since it uses less digits than its factorization.

409959040 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 10581 (or 10569 counting only the distinct ones).

The product of its (nonzero) digits is 58320, while the sum is 40.

The square root of 409959040 is about 20247.4452709471. The cubic root of 409959040 is about 742.8711442839.

The spelling of 409959040 in words is "four hundred nine million, nine hundred fifty-nine thousand, forty".