122112 has 54 divisors (see below), whose sum is σ = 358722. Its totient is φ = 39936.

The previous prime is 122099. The next prime is 122117. The reversal of 122112 is 211221.

Adding to 122112 its reverse (211221), we get a palindrome (333333).

It can be written as a sum of positive squares in only one way, i.e., 112896 + 9216 = 336^2 + 96^2 .

It is a super-2 number, since 2×122112^{2} = 29822681088, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is a nude number because it is divisible by every one of its digits and also a Zuckerman number because it is divisible by the product of its digits.

It is an Ulam number.

It is a junction number, because it is equal to *n*+sod(*n*) for *n* = 122094 and 122103.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (122117) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 2278 + ... + 2330.

It is an arithmetic number, because the mean of its divisors is an integer number (6643).

2^{122112} is an apocalyptic number.

122112 is a gapful number since it is divisible by the number (12) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 122112, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (179361).

122112 is an abundant number, since it is smaller than the sum of its proper divisors (236610).

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

122112 is an equidigital number, since it uses as much as digits as its factorization.

122112 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 75 (or 58 counting only the distinct ones).

The product of its digits is 8, while the sum is 9.

The square root of 122112 is about 349.4452746855. The cubic root of 122112 is about 49.6119291460.

The spelling of 122112 in words is "one hundred twenty-two thousand, one hundred twelve", and thus it is an iban number.

Divisors: 1 2 3 4 6 8 9 12 16 18 24 32 36 48 53 64 72 96 106 128 144 159 192 212 256 288 318 384 424 477 576 636 768 848 954 1152 1272 1696 1908 2304 2544 3392 3816 5088 6784 7632 10176 13568 15264 20352 30528 40704 61056 122112

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