409649280768 has 1440 divisors, whose sum is σ = 1595536588800. Its totient is φ = 101642895360.

The previous prime is 409649280751. The next prime is 409649280809. The reversal of 409649280768 is 867082946904.

409649280768 is a `hidden beast` number, since 4 + 0 + 9 + 6 + 492 + 80 + 7 + 68 = 666.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is a congruent number.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 159 ways as a sum of consecutive naturals, for example, 2749323958 + ... + 2749324106.

It is an arithmetic number, because the mean of its divisors is an integer number (1108011520).

Almost surely, 2^409649280768 is an apocalyptic number.

409649280768 is a gapful number since it is divisible by the number (48) 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 409649280768, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (797768294400).

409649280768 is an abundant number, since it is smaller than the sum of its proper divisors (1185887308032).

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

409649280768 is a wasteful number, since it uses less digits than its factorization.

409649280768 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 275 (or 252 counting only the distinct ones).

The product of its (nonzero) digits is 41803776, while the sum is 63.

The spelling of 409649280768 in words is "four hundred nine billion, six hundred forty-nine million, two hundred eighty thousand, seven hundred sixty-eight".