409581120 has 224 divisors, whose sum is σ = 1439923968. Its totient is φ = 97984512.

The previous prime is 409581113. The next prime is 409581121. The reversal of 409581120 is 21185904.

409581120 = T₃₉₉ + T₄₀₀ + ... + T₁₃₆₀.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is not an unprimeable number, because it can be changed into a prime (409581121) by changing a digit.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 461317 + ... + 462203.

It is an arithmetic number, because the mean of its divisors is an integer number (6428232).

Almost surely, 2^409581120 is an apocalyptic number.

409581120 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 409581120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (719961984).

409581120 is an abundant number, since it is smaller than the sum of its proper divisors (1030342848).

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

409581120 is a wasteful number, since it uses less digits than its factorization.

409581120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 957 (or 947 counting only the distinct ones).

The product of its (nonzero) digits is 2880, while the sum is 30.

The square root of 409581120 is about 20238.1105837477. The cubic root of 409581120 is about 742.6428026302.

The spelling of 409581120 in words is "four hundred nine million, five hundred eighty-one thousand, one hundred twenty".