133128 has 36 divisors (see below), whose sum is σ = 369135. Its totient is φ = 43344.

The previous prime is 133121. The next prime is 133153. The reversal of 133128 is 821331.

It is a powerful number, because all its prime factors have an exponent greater than 1 and also an Achilles number because it is not a perfect power.

It can be written as a sum of positive squares in only one way, i.e., 66564 + 66564 = 258^2 + 258^2 .

It is a tau number, because it is divible by the number of its divisors (36).

It is an ABA number since it can be written as A⋅B^A, here for A=2, B=258.

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

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

Its product of digits (144) is a multiple of the sum of its prime divisors (48).

It is a self number, because there is not a number n which added to its sum of digits gives 133128.

It is not an unprimeable number, because it can be changed into a prime (133121) by changing a digit.

133128 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (3) of ones.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 3075 + ... + 3117.

2¹³³¹²⁸ is an apocalyptic number.

133128 is a gapful number since it is divisible by the number (18) 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 133128

133128 is an abundant number, since it is smaller than the sum of its proper divisors (236007).

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

133128 is a wasteful number, since it uses less digits than its factorization.

133128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 98 (or 48 counting only the distinct ones).

The product of its digits is 144, while the sum is 18.

The square root of 133128 is about 364.8670990923. The cubic root of 133128 is about 51.0610572076.

Multiplying 133128 by its sum of digits (18), we get a square (2396304 = 1548²).

133128 divided by its sum of digits (18) gives a square (7396 = 86²).

Adding to 133128 its reverse (821331), we get a palindrome (954459).

The spelling of 133128 in words is "one hundred thirty-three thousand, one hundred twenty-eight".