32761 has 3 divisors (see below), whose sum is σ = 32943. Its totient is φ = 32580.

The previous prime is 32749. The next prime is 32771. The reversal of 32761 is 16723.

32761 = T₁₈₀ + T₁₈₁.

The square root of 32761 is 181.

It is a perfect power (a square), and thus also a powerful number.

32761 is nontrivially palindromic in base 12.

It is a semiprime because it is the product of two primes, and also a brilliant number, because the two primes have the same length, and also an emirpimes, since its reverse is a distinct semiprime: 16723 = 7 ⋅2389.

It can be written as a sum of positive squares in only one way, i.e., 361 + 32400 = 19^2 + 180^2 .

It is not a de Polignac number, because 32761 - 2⁷ = 32633 is a prime.

It is an alternating number because its digits alternate between odd and even.

It is a Duffinian number.

32761 is a lucky number.

It is a nialpdrome in base 8.

It is not an unprimeable number, because it can be changed into a prime (32771) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 91 + ... + 271.

It is an arithmetic number, because the mean of its divisors is an integer number (10981).

32761 is a Friedman number, since it can be written as (2^(1-6))^(-3)-7, using all its digits and the basic arithmetic operations.

2³²⁷⁶¹ is an apocalyptic number.

32761 is the 181-st square number.

32761 is the 105-th hex number and also the 91-st centered octagonal number.

It is an amenable number.

32761 is a deficient number, since it is larger than the sum of its proper divisors (182).

32761 is an frugal number, since it uses more digits than its factorization.

32761 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 362 (or 181 counting only the distinct ones).

The product of its digits is 252, while the sum is 19.

The cubic root of 32761 is about 31.9977211919.

The spelling of 32761 in words is "thirty-two thousand, seven hundred sixty-one".