409605504 has 192 divisors, whose sum is σ = 1381406400. Its totient is φ = 106337280.

The previous prime is 409605499. The next prime is 409605509. The reversal of 409605504 is 405506904.

It is an interprime number because it is at equal distance from previous prime (409605499) and next prime (409605509).

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

It is a Harshad number since it is a multiple of its sum of digits (33).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409605509) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 205987 + ... + 207965.

It is an arithmetic number, because the mean of its divisors is an integer number (7194825).

Almost surely, 2^409605504 is an apocalyptic number.

409605504 is a gapful number since it is divisible by the number (44) 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 409605504, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (690703200).

409605504 is an abundant number, since it is smaller than the sum of its proper divisors (971800896).

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

409605504 is a wasteful number, since it uses less digits than its factorization.

409605504 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2021 (or 2002 counting only the distinct ones).

The product of its (nonzero) digits is 21600, while the sum is 33.

The square root of 409605504 is about 20238.7130025602. The cubic root of 409605504 is about 742.6575398351.

It can be divided in two parts, 40960 and 5504, that added together give a palindrome (46464).

The spelling of 409605504 in words is "four hundred nine million, six hundred five thousand, five hundred four".