193688 has 32 divisors (see below), whose sum is σ = 414720. Its totient is φ = 84000.

The previous prime is 193679. The next prime is 193703. The reversal of 193688 is 886391.

193688 is digitally balanced in base 2 and base 3, because in such bases it contains all the possibile digits an equal number of times.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 193688.

It is an unprimeable number.

193688 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 2693 + ... + 2763.

It is an arithmetic number, because the mean of its divisors is an integer number (12960).

2¹⁹³⁶⁸⁸ 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 193688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (207360).

193688 is an abundant number, since it is smaller than the sum of its proper divisors (221032).

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

193688 is a wasteful number, since it uses less digits than its factorization.

193688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 119 (or 115 counting only the distinct ones).

The product of its digits is 10368, while the sum is 35.

The square root of 193688 is about 440.0999886389. The cubic root of 193688 is about 57.8585534672.

The spelling of 193688 in words is "one hundred ninety-three thousand, six hundred eighty-eight".