199722112128 has 1512 divisors, whose sum is σ = 805029536115. Its totient is φ = 49145564160.

The previous prime is 199722112067. The next prime is 199722112153. The reversal of 199722112128 is 821211227991.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 99861056064 + 99861056064 = 316008^2 + 316008^2 .

It is a tau number, because it is divible by the number of its divisors (1512).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=316008.

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

Its product of digits (72576) is a multiple of the sum of its prime divisors (42).

It is an unprimeable number.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 10511690103 + ... + 10511690121.

Almost surely, 2^199722112128 is an apocalyptic number.

199722112128 is a gapful number since it is divisible by the number (18) 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 199722112128

199722112128 is an abundant number, since it is smaller than the sum of its proper divisors (605307423987).

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

199722112128 is an equidigital number, since it uses as much as digits as its factorization.

199722112128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 106 (or 42 counting only the distinct ones).

The product of its digits is 72576, while the sum is 45.

The spelling of 199722112128 in words is "one hundred ninety-nine billion, seven hundred twenty-two million, one hundred twelve thousand, one hundred twenty-eight".