409565520 has 720 divisors, whose sum is σ = 1852381440. Its totient is φ = 80123904.

The previous prime is 409565491. The next prime is 409565537. The reversal of 409565520 is 25565904.

409565520 is a `hidden beast` number, since 40 + 9 + 565 + 52 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (720).

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 143 ways as a sum of consecutive naturals, for example, 8714137 + ... + 8714183.

It is an arithmetic number, because the mean of its divisors is an integer number (2572752).

Almost surely, 2^409565520 is an apocalyptic number.

409565520 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 409565520, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (926190720).

409565520 is an abundant number, since it is smaller than the sum of its proper divisors (1442815920).

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

409565520 is a wasteful number, since it uses less digits than its factorization.

409565520 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 112 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 54000, while the sum is 36.

The square root of 409565520 is about 20237.7251686053. The cubic root of 409565520 is about 742.6333739934.

It can be divided in two parts, 4095 and 65520, that multiplied together give a square (268304400 = 16380²).

The spelling of 409565520 in words is "four hundred nine million, five hundred sixty-five thousand, five hundred twenty".