199953 has 12 divisors (see below), whose sum is σ = 311220. Its totient is φ = 122976.

The previous prime is 199933. The next prime is 199961. The reversal of 199953 is 359991.

199953 is nontrivially palindromic in base 14.

It can be written as a sum of positive squares in 2 ways, for example, as 33489 + 166464 = 183^2 + 408^2 .

It is not a de Polignac number, because 199953 - 2⁵ = 199921 is a prime.

199953 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (199933) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 738 + ... + 971.

It is an arithmetic number, because the mean of its divisors is an integer number (25935).

2¹⁹⁹⁹⁵³ is an apocalyptic number.

199953 is a gapful number since it is divisible by the number (13) formed by its first and last digit.

It is an amenable number.

199953 is a deficient number, since it is larger than the sum of its proper divisors (111267).

199953 is a wasteful number, since it uses less digits than its factorization.

199953 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1728 (or 1725 counting only the distinct ones).

The product of its digits is 10935, while the sum is 36.

The square root of 199953 is about 447.1610448150. The cubic root of 199953 is about 58.4757734442.

The spelling of 199953 in words is "one hundred ninety-nine thousand, nine hundred fifty-three".