165888 has 60 divisors (see below), whose sum is σ = 495495. Its totient is φ = 55296.

The previous prime is 165887. The next prime is 165901. The reversal of 165888 is 888561.

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 is a Jordan-Polya number, since it can be written as (4!)^{3} ⋅ 3! ⋅ 2!.

165888 is nontrivially palindromic in base 15.

It can be written as a sum of positive squares in only one way, i.e., 82944 + 82944 = 288^2 + 288^2 .

It is an ABA number since it can be written as A⋅B^{A}, here for A=2, B=288.

It is a Harshad number since it is a multiple of its sum of digits (36).

Its product of digits (15360) is a multiple of the sum of its prime divisors (5).

It is a nialpdrome in base 6 and base 12.

It is an inconsummate number, since it does not exist a number *n* which divided by its sum of digits gives 165888.

It is not an unprimeable number, because it can be changed into a prime (165883) by changing a digit.

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 4 ways as a sum of consecutive naturals, for example, 55295 + 55296 + 55297.

165888 is a Friedman number, since it can be written as (8+8)*8*6^(5-1), using all its digits and the basic arithmetic operations.

2^{165888} is an apocalyptic number.

165888 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 165888

165888 is an abundant number, since it is smaller than the sum of its proper divisors (329607).

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

165888 is an frugal number, since it uses more digits than its factorization.

165888 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 34 (or 5 counting only the distinct ones).

The product of its digits is 15360, while the sum is 36.

The square root of 165888 is about 407.2935059635. The cubic root of 165888 is about 54.9462836426.

The spelling of 165888 in words is "one hundred sixty-five thousand, eight hundred eighty-eight".

Divisors: 1 2 3 4 6 8 9 12 16 18 24 27 32 36 48 54 64 72 81 96 108 128 144 162 192 216 256 288 324 384 432 512 576 648 768 864 1024 1152 1296 1536 1728 2048 2304 2592 3072 3456 4608 5184 6144 6912 9216 10368 13824 18432 20736 27648 41472 55296 82944 165888

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