90688 has 28 divisors (see below), whose sum is σ = 195580. Its totient is φ = 41472.

The previous prime is 90679. The next prime is 90697. The reversal of 90688 is 88609.

It is an interprime number because it is at equal distance from previous prime (90679) and next prime (90697).

It can be written as a sum of positive squares in 2 ways, for example, as 36864 + 53824 = 192^2 + 232^2 .

It is an unprimeable number.

90688 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 (5) of ones.

It is a polite number, since it can be written in 3 ways as a sum of consecutive naturals, for example, 778 + ... + 886.

It is an arithmetic number, because the mean of its divisors is an integer number (6985).

2⁹⁰⁶⁸⁸ is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 90688, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (97790).

90688 is an abundant number, since it is smaller than the sum of its proper divisors (104892).

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

90688 is a wasteful number, since it uses less digits than its factorization.

90688 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 134 (or 124 counting only the distinct ones).

The product of its (nonzero) digits is 3456, while the sum is 31.

The square root of 90688 is about 301.1444835955. The cubic root of 90688 is about 44.9279505469.

The spelling of 90688 in words is "ninety thousand, six hundred eighty-eight".