409048416 has 288 divisors, whose sum is σ = 1430956800. Its totient is φ = 108241920.

The previous prime is 409048411. The next prime is 409048427. The reversal of 409048416 is 614840904.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (288).

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

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409048411) by changing a digit.

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 47 ways as a sum of consecutive naturals, for example, 2259846 + ... + 2260026.

It is an arithmetic number, because the mean of its divisors is an integer number (4968600).

Almost surely, 2^409048416 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 409048416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (715478400).

409048416 is an abundant number, since it is smaller than the sum of its proper divisors (1021908384).

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

409048416 is a wasteful number, since it uses less digits than its factorization.

409048416 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 282 (or 271 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

The square root of 409048416 is about 20224.9453892959. The cubic root of 409048416 is about 742.3207008480.

The spelling of 409048416 in words is "four hundred nine million, forty-eight thousand, four hundred sixteen".