10585 has 8 divisors (see below), whose sum is σ = 13320. Its totient is φ = 8064.

The previous prime is 10567. The next prime is 10589. The reversal of 10585 is 58501.

It can be divided in two parts, 105 and 85, that added together give a triangular number (190 = T_{19}).

10585 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

10585 is a nontrivial binomial coefficient, being equal to C(146, 2).

It can be written as a sum of positive squares in 4 ways, for example, as 1369 + 9216 = 37^2 + 96^2 .

It is a sphenic number, since it is the product of 3 distinct primes.

It is a 3-Lehmer number, since φ(10585) divides (10585-1)^{3}.

It is a cyclic number.

It is a Carmichael number.

It is not a de Polignac number, because 10585 - 2^{7} = 10457 is a prime.

It is a super-2 number, since 2×10585^{2} = 224084450, which contains 22 as substring.

It is an alternating number because its digits alternate between odd and even.

10585 is an undulating number in base 12.

10585 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (10589) 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 7 ways as a sum of consecutive naturals, for example, 109 + ... + 181.

It is an arithmetic number, because the mean of its divisors is an integer number (1665).

It is a Poulet number, since it divides 2^{10584}-1.

2^{10585} is an apocalyptic number.

10585 is the 145-th triangular number and also the 73-rd hexagonal number.

10585 is the 49-th centered nonagonal number.

It is an amenable number.

10585 is a deficient number, since it is larger than the sum of its proper divisors (2735).

10585 is an equidigital number, since it uses as much as digits as its factorization.

10585 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 107.

The product of its (nonzero) digits is 200, while the sum is 19.

The square root of 10585 is about 102.8834291808. The cubic root of 10585 is about 21.9565257171.

The spelling of 10585 in words is "ten thousand, five hundred eighty-five".

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