1513728000 has 480 divisors, whose sum is σ = 5719994280. Its totient is φ = 398131200.

The previous prime is 1513727981. The next prime is 1513728001. The reversal of 1513728000 is 8273151.

1513728000 is a `hidden beast` number, since 1 + 513 + 72 + 80 + 0 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 491774976 + 1021953024 = 22176^2 + 31968^2 .

It is a tau number, because it is divible by the number of its divisors (480).

It is a Harshad number since it is a multiple of its sum of digits (27).

It is not an unprimeable number, because it can be changed into a prime (1513728001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 39 ways as a sum of consecutive naturals, for example, 20735964 + ... + 20736036.

Almost surely, 2^1513728000 is an apocalyptic number.

1513728000 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 1513728000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2859997140).

1513728000 is an abundant number, since it is smaller than the sum of its proper divisors (4206266280).

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

1513728000 is an frugal number, since it uses more digits than its factorization.

1513728000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 122 (or 83 counting only the distinct ones).

The product of its (nonzero) digits is 1680, while the sum is 27.

The square root of 1513728000 is about 38906.6575279861. The cubic root of 1513728000 is about 1148.1957846142.

The spelling of 1513728000 in words is "one billion, five hundred thirteen million, seven hundred twenty-eight thousand".