133305120 has 144 divisors (see below), whose sum is σ = 489965112. Its totient is φ = 32808960.

The previous prime is 133305119. The next prime is 133305167. The reversal of 133305120 is 21503331.

It can be written as a sum of positive squares in 4 ways, for example, as 41835024 + 91470096 = 6468^2 + 9564^2 .

It is a tau number, because it is divible by the number of its divisors (144).

It is a super-3 number, since 3×133305120³ (a number of 25 digits) contains 333 as substring.

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

It is a junction number, because it is equal to n+sod(n) for n = 133305093 and 133305102.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 15160 + ... + 22280.

Almost surely, 2^133305120 is an apocalyptic number.

133305120 is a gapful number since it is divisible by the number (10) 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 133305120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (244982556).

133305120 is an abundant number, since it is smaller than the sum of its proper divisors (356659992).

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

133305120 is a wasteful number, since it uses less digits than its factorization.

133305120 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7155 (or 7144 counting only the distinct ones).

The product of its (nonzero) digits is 270, while the sum is 18.

The square root of 133305120 is about 11545.7836459896. The cubic root of 133305120 is about 510.8369188147.

Adding to 133305120 its reverse (21503331), we get a palindrome (154808451).

The spelling of 133305120 in words is "one hundred thirty-three million, three hundred five thousand, one hundred twenty".