83088000 has 192 divisors, whose sum is σ = 298906920. Its totient is φ = 22118400.

The previous prime is 83087999. The next prime is 83088001. The reversal of 83088000 is 88038.

It is an interprime number because it is at equal distance from previous prime (83087999) and next prime (83088001).

It can be written as a sum of positive squares in 4 ways, for example, as 52881984 + 30206016 = 7272^2 + 5496^2 .

It is a tau number, because it is divible by the number of its divisors (192).

It is not an unprimeable number, because it can be changed into a prime (83088001) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 143712 + ... + 144288.

Almost surely, 2^83088000 is an apocalyptic number.

83088000 is a gapful number since it is divisible by the number (80) 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 83088000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (149453460).

83088000 is an abundant number, since it is smaller than the sum of its proper divisors (215818920).

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

83088000 is a wasteful number, since it uses less digits than its factorization.

83088000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 612 (or 587 counting only the distinct ones).

The product of its (nonzero) digits is 1536, while the sum is 27.

The square root of 83088000 is about 9115.2619271198. The cubic root of 83088000 is about 436.3611742285.

The spelling of 83088000 in words is "eighty-three million, eighty-eight thousand".