13505 has 8 divisors (see below), whose sum is σ = 16872. Its totient is φ = 10368.

The previous prime is 13499. The next prime is 13513. The reversal of 13505 is 50531.

13505 is digitally balanced in base 3 and base 6, because in such bases it contains all the possibile digits an equal number of times.

It can be written as a sum of positive squares in 4 ways, for example, as 4096 + 9409 = 64^2 + 97^2 .

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 13505 - 2⁶ = 13441 is a prime.

13505 is strictly pandigital in base 6.

It is a Curzon number.

It is a self number, because there is not a number n which added to its sum of digits gives 13505.

It is an unprimeable number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 149 + ... + 221.

It is an arithmetic number, because the mean of its divisors is an integer number (2109).

2¹³⁵⁰⁵ is an apocalyptic number.

It is an amenable number.

13505 is a deficient number, since it is larger than the sum of its proper divisors (3367).

13505 is an equidigital number, since it uses as much as digits as its factorization.

13505 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 115.

The product of its (nonzero) digits is 75, while the sum is 14.

The square root of 13505 is about 116.2110149685. The cubic root of 13505 is about 23.8139550483.

The spelling of 13505 in words is "thirteen thousand, five hundred five".