32513 has 8 divisors (see below), whose sum is σ = 36456. Its totient is φ = 28800.

The previous prime is 32507. The next prime is 32531. The reversal of 32513 is 31523.

32513 = 127² + 128².

It can be written as a sum of positive squares in 4 ways, for example, as 4624 + 27889 = 68^2 + 167^2 .

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 32513 - 2⁴ = 32497 is a prime.

It is a Duffinian number.

It is a Curzon number.

It is a plaindrome in base 11.

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 32513.

It is not an unprimeable number, because it can be changed into a prime (32503) by changing a digit.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 503 + ... + 563.

It is an arithmetic number, because the mean of its divisors is an integer number (4557).

It is a Proth number, since it is equal to 127 ⋅ 2⁸ + 1 and 127 < 2⁸.

2³²⁵¹³ is an apocalyptic number.

32513 is the 128-th centered square number.

It is an amenable number.

32513 is a deficient number, since it is larger than the sum of its proper divisors (3943).

32513 is a wasteful number, since it uses less digits than its factorization.

32513 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 digits is 90, while the sum is 14.

The square root of 32513 is about 180.3136156811. The cubic root of 32513 is about 31.9167759300.

Subtracting from 32513 its product of digits (90), we obtain a palindrome (32423).

Subtracting from 32513 its reverse (31523), we obtain a triangular number (990 = T₄₄).

It can be divided in two parts, 325 and 13, that multiplied together give a square (4225 = 65²).

The spelling of 32513 in words is "thirty-two thousand, five hundred thirteen".