221312 has 64 divisors (see below), whose sum is σ = 571200. Its totient is φ = 82944.

The previous prime is 221311. The next prime is 221317. The reversal of 221312 is 213122.

It is a happy number.

It is a tau number, because it is divible by the number of its divisors (64).

It is a junction number, because it is equal to n+sod(n) for n = 221293 and 221302.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (221311) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 11639 + ... + 11657.

It is an arithmetic number, because the mean of its divisors is an integer number (8925).

2²²¹³¹² 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 221312, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (285600).

221312 is an abundant number, since it is smaller than the sum of its proper divisors (349888).

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

221312 is a wasteful number, since it uses less digits than its factorization.

221312 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 53 (or 41 counting only the distinct ones).

The product of its digits is 24, while the sum is 11.

The square root of 221312 is about 470.4380936957. The cubic root of 221312 is about 60.4878740810.

Adding to 221312 its reverse (213122), we get a palindrome (434434).

It can be divided in two parts, 2 and 21312, that multiplied together give a palindrome (42624).

The spelling of 221312 in words is "two hundred twenty-one thousand, three hundred twelve", and thus it is an iban number.