409505241600 has 1920 divisors, whose sum is σ = 1918002240000. Its totient is φ = 83235962880.

The previous prime is 409505241581. The next prime is 409505241611. The reversal of 409505241600 is 6142505904.

409505241600 is a `hidden beast` number, since 4 + 0 + 9 + 5 + 0 + 5 + 2 + 41 + 600 = 666.

It is a tau number, because it is divible by the number of its divisors (1920).

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

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 912038176 + ... + 912038624.

It is an arithmetic number, because the mean of its divisors is an integer number (998959500).

Almost surely, 2^409505241600 is an apocalyptic number.

409505241600 is a gapful number since it is divisible by the number (40) 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 409505241600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (959001120000).

409505241600 is an abundant number, since it is smaller than the sum of its proper divisors (1508496998400).

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

409505241600 is a wasteful number, since it uses less digits than its factorization.

409505241600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 535 (or 508 counting only the distinct ones).

The product of its (nonzero) digits is 43200, while the sum is 36.

The spelling of 409505241600 in words is "four hundred nine billion, five hundred five million, two hundred forty-one thousand, six hundred".