105624 has 40 divisors (see below), whose sum is σ = 297660. Its totient is φ = 34992.

The previous prime is 105619. The next prime is 105649. The reversal of 105624 is 426501.

105624 = 2³ + 3³ + ... + 25³.

It is a happy number.

It is a Cunningham number, because it is equal to 325²-1.

It is a super-2 number, since 2×105624² = 22312858752, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a plaindrome in base 5.

It is a zygodrome in base 5.

It is a junction number, because it is equal to n+sod(n) for n = 105597 and 105606.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 9 ways as a sum of consecutive naturals, for example, 567 + ... + 729.

105624 is a Friedman number, since it can be written as 650^2/4-1, using all its digits and the basic arithmetic operations.

2¹⁰⁵⁶²⁴ 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 105624, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (148830).

105624 is an abundant number, since it is smaller than the sum of its proper divisors (192036).

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

105624 is a wasteful number, since it uses less digits than its factorization.

105624 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 181 (or 168 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 105624 is about 324.9984615348. The cubic root of 105624 is about 47.2702105528.

It can be divided in two parts, 105 and 624, that added together give a 6-th power (729 = 3⁶).

The spelling of 105624 in words is "one hundred five thousand, six hundred twenty-four".