409578624 has 192 divisors, whose sum is σ = 1450962240. Its totient is φ = 107993088.

The previous prime is 409578619. The next prime is 409578661. The reversal of 409578624 is 426875904.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (192).

It is a self number, because there is not a number n which added to its sum of digits gives 409578624.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 102879 + ... + 106785.

It is an arithmetic number, because the mean of its divisors is an integer number (7557095).

Almost surely, 2^409578624 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 409578624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (725481120).

409578624 is an abundant number, since it is smaller than the sum of its proper divisors (1041383616).

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

409578624 is a wasteful number, since it uses less digits than its factorization.

409578624 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3947 (or 3932 counting only the distinct ones).

The product of its (nonzero) digits is 483840, while the sum is 45.

The square root of 409578624 is about 20238.0489178181. The cubic root of 409578624 is about 742.6412940644.

The spelling of 409578624 in words is "four hundred nine million, five hundred seventy-eight thousand, six hundred twenty-four".