72361 has 3 divisors (see below), whose sum is σ = 72631. Its totient is φ = 72092.

The previous prime is 72353. The next prime is 72367. The reversal of 72361 is 16327.

72361 = T₂₆₈ + T₂₆₉.

The square root of 72361 is 269.

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

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: 16327 = 29 ⋅563.

It can be written as a sum of positive squares in only one way, i.e., 4761 + 67600 = 69^2 + 260^2 .

It is not a de Polignac number, because 72361 - 2³ = 72353 is a prime.

It is a super-2 number, since 2×72361² = 10472228642, which contains 22 as substring.

It is an Ulam number.

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (72367) by changing a digit.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 135 + ... + 403.

2⁷²³⁶¹ is an apocalyptic number.

72361 is the 269-th square number.

72361 is the 135-th centered octagonal number.

It is an amenable number.

72361 is a deficient number, since it is larger than the sum of its proper divisors (270).

72361 is an frugal number, since it uses more digits than its factorization.

72361 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 538 (or 269 counting only the distinct ones).

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

The cubic root of 72361 is about 41.6710893083.

Adding to 72361 its reverse (16327), we get a palindrome (88688).

It can be divided in two parts, 723 and 61, that added together give a square (784 = 28²).

The spelling of 72361 in words is "seventy-two thousand, three hundred sixty-one".