409449406464 has 700 divisors, whose sum is σ = 1432556027694. Its totient is φ = 116530348032.

The previous prime is 409449406427. The next prime is 409449406517. The reversal of 409449406464 is 464604944904.

409449406464 is a `hidden beast` number, since 4 + 0 + 94 + 4 + 94 + 0 + 6 + 464 = 666.

It can be written as a sum of positive squares in only one way, i.e., 230215716864 + 179233689600 = 479808^2 + 423360^2 .

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a self number, because there is not a number n which added to its sum of digits gives 409449406464.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 49 ways as a sum of consecutive naturals, for example, 1593188224 + ... + 1593188480.

Almost surely, 2^409449406464 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 409449406464, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (716278013847).

409449406464 is an abundant number, since it is smaller than the sum of its proper divisors (1023106621230).

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

409449406464 is an frugal number, since it uses more digits than its factorization.

409449406464 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 323 (or 269 counting only the distinct ones).

The product of its (nonzero) digits is 11943936, while the sum is 54.

The spelling of 409449406464 in words is "four hundred nine billion, four hundred forty-nine million, four hundred six thousand, four hundred sixty-four".