13515 has 16 divisors (see below), whose sum is σ = 23328. Its totient is φ = 6656.

The previous prime is 13513. The next prime is 13523. The reversal of 13515 is 51531.

Adding to 13515 its sum of digits (15), we get a triangular number (13530 = T_{164}).

It can be divided in two parts, 135 and 15, that multiplied together give a square (2025 = 45^{2}).

13515 is nontrivially palindromic in base 2.

13515 is digitally balanced in base 3, because in such base it contains all the possibile digits an equal number of times.

It is a cyclic number.

It is not a de Polignac number, because 13515 - 2^{1} = 13513 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (15).

It is a nude number because it is divisible by every one of its digits.

13515 is a lucky number.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 13494 and 13503.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (13513) by changing a digit.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 229 + ... + 281.

It is an arithmetic number, because the mean of its divisors is an integer number (1458).

It is the magic constant of a 30 × 30 magic square.

2^{13515} is an apocalyptic number.

13515 is a gapful number since it is divisible by the number (15) formed by its first and last digit.

13515 is a deficient number, since it is larger than the sum of its proper divisors (9813).

13515 is a wasteful number, since it uses less digits than its factorization.

13515 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 78.

The product of its digits is 75, while the sum is 15.

The square root of 13515 is about 116.2540321881. The cubic root of 13515 is about 23.8198314100.

The spelling of 13515 in words is "thirteen thousand, five hundred fifteen".

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