312813113221728 has 960 divisors, whose sum is σ = 1140497827983360. Its totient is φ = 82063376252928.

The previous prime is 312813113221673. The next prime is 312813113221733. The reversal of 312813113221728 is 827122311318213.

312813113221728 is a `hidden beast` number, since 3 + 1 + 2 + 8 + 1 + 311 + 322 + 1 + 7 + 2 + 8 = 666.

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 159 ways as a sum of consecutive naturals, for example, 11446183168 + ... + 11446210496.

It is an arithmetic number, because the mean of its divisors is an integer number (1188018570816).

Almost surely, 2^{312813113221728} 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 312813113221728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (570248913991680).

312813113221728 is an abundant number, since it is smaller than the sum of its proper divisors (827684714761632).

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

312813113221728 is a wasteful number, since it uses less digits than its factorization.

312813113221728 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 28281 (or 28264 counting only the distinct ones).

The product of its digits is 193536, while the sum is 45.

The spelling of 312813113221728 in words is "three hundred twelve trillion, eight hundred thirteen billion, one hundred thirteen million, two hundred twenty-one thousand, seven hundred twenty-eight".