81624 has 32 divisors (see below), whose sum is σ = 216000. Its totient is φ = 25632.

The previous prime is 81619. The next prime is 81629. The reversal of 81624 is 42618.

81624 is nontrivially palindromic in base 7.

It is an interprime number because it is at equal distance from previous prime (81619) and next prime (81629).

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

It is one of the 548 Lynch-Bell numbers.

It is a self number, because there is not a number n which added to its sum of digits gives 81624.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (81629) 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, 367 + ... + 545.

It is an arithmetic number, because the mean of its divisors is an integer number (6750).

2⁸¹⁶²⁴ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (108000).

81624 is an abundant number, since it is smaller than the sum of its proper divisors (134376).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

81624 is a wasteful number, since it uses less digits than its factorization.

81624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 207 (or 203 counting only the distinct ones).

The product of its digits is 384, while the sum is 21.

The square root of 81624 is about 285.6991424558. The cubic root of 81624 is about 43.3783096468.

The spelling of 81624 in words is "eighty-one thousand, six hundred twenty-four".