193664 has 32 divisors (see below), whose sum is σ = 413100. Its totient is φ = 90112.

The previous prime is 193663. The next prime is 193679. The reversal of 193664 is 466391.

It can be written as a sum of positive squares in 2 ways, for example, as 193600 + 64 = 440^2 + 8^2 .

It is a tau number, because it is divible by the number of its divisors (32).

Its product of digits (3888) is a multiple of the sum of its prime divisors (108).

It is a plaindrome in base 11.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (193663) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 2132 + ... + 2220.

2¹⁹³⁶⁶⁴ 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 193664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (206550).

193664 is an abundant number, since it is smaller than the sum of its proper divisors (219436).

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

193664 is an equidigital number, since it uses as much as digits as its factorization.

193664 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 120 (or 108 counting only the distinct ones).

The product of its digits is 3888, while the sum is 29.

The square root of 193664 is about 440.0727212632. The cubic root of 193664 is about 57.8561636054.

It can be divided in two parts, 1936 and 64, that multiplied together give a square (123904 = 352²).

The spelling of 193664 in words is "one hundred ninety-three thousand, six hundred sixty-four".