409188049920 has 792 divisors, whose sum is σ = 1587227571384. Its totient is φ = 100615716864.

The previous prime is 409188049891. The next prime is 409188049937. The reversal of 409188049920 is 29940881904.

409188049920 is a `hidden beast` number, since 40 + 9 + 18 + 80 + 499 + 20 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 9197577216 + 399990472704 = 95904^2 + 632448^2 .

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

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 71 ways as a sum of consecutive naturals, for example, 436699692 + ... + 436700628.

Almost surely, 2^409188049920 is an apocalyptic number.

409188049920 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 409188049920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (793613785692).

409188049920 is an abundant number, since it is smaller than the sum of its proper divisors (1178039521464).

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

409188049920 is an frugal number, since it uses more digits than its factorization.

409188049920 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 999 (or 960 counting only the distinct ones).

The product of its (nonzero) digits is 1492992, while the sum is 54.

The spelling of 409188049920 in words is "four hundred nine billion, one hundred eighty-eight million, forty-nine thousand, nine hundred twenty".