193305 has 24 divisors (see below), whose sum is σ = 361152. Its totient is φ = 88032.

The previous prime is 193301. The next prime is 193327. The reversal of 193305 is 503391.

193305 = 95² + 96² + ... + 112².

It is not a de Polignac number, because 193305 - 2² = 193301 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (21).

It is a Curzon number.

193305 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (193301) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 604 + ... + 866.

It is an arithmetic number, because the mean of its divisors is an integer number (15048).

2¹⁹³³⁰⁵ is an apocalyptic number.

193305 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

It is an amenable number.

193305 is a deficient number, since it is larger than the sum of its proper divisors (167847).

193305 is a wasteful number, since it uses less digits than its factorization.

193305 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 285 (or 278 counting only the distinct ones).

The product of its (nonzero) digits is 405, while the sum is 21.

The square root of 193305 is about 439.6646449284. The cubic root of 193305 is about 57.8203916668.

Adding to 193305 its reverse (503391), we get a palindrome (696696).

The spelling of 193305 in words is "one hundred ninety-three thousand, three hundred five".