409601664 has 128 divisors (see below), whose sum is σ = 1261699200. Its totient is φ = 130572288.

The previous prime is 409601657. The next prime is 409601669. The reversal of 409601664 is 466106904.

409601664 is a `hidden beast` number, since 40 + 9 + 601 + 6 + 6 + 4 = 666.

It is a tau number, because it is divible by the number of its divisors (128).

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

It is not an unprimeable number, because it can be changed into a prime (409601669) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 76912 + ... + 82064.

It is an arithmetic number, because the mean of its divisors is an integer number (9857025).

Almost surely, 2^409601664 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 409601664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (630849600).

409601664 is an abundant number, since it is smaller than the sum of its proper divisors (852097536).

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

409601664 is a wasteful number, since it uses less digits than its factorization.

409601664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 5199 (or 5181 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 36.

The square root of 409601664 is about 20238.6181346455. The cubic root of 409601664 is about 742.6552190543.

It can be divided in two parts, 40960 and 1664, that added together give a palindrome (42624).

The spelling of 409601664 in words is "four hundred nine million, six hundred one thousand, six hundred sixty-four".