90405 has 36 divisors (see below), whose sum is σ = 186732. Its totient is φ = 40320.

The previous prime is 90403. The next prime is 90407. The reversal of 90405 is 50409.

90405 is nontrivially palindromic in base 4.

It is an interprime number because it is at equal distance from previous prime (90403) and next prime (90407).

It can be written as a sum of positive squares in 2 ways, for example, as 15876 + 74529 = 126^2 + 273^2 .

It is not a de Polignac number, because 90405 - 2¹ = 90403 is a prime.

90405 is a modest number, since divided by 405 gives 90 as remainder.

It is a Curzon number.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (90401) 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 35 ways as a sum of consecutive naturals, for example, 2185 + ... + 2225.

It is an arithmetic number, because the mean of its divisors is an integer number (5187).

2⁹⁰⁴⁰⁵ is an apocalyptic number.

It is an amenable number.

90405 is an abundant number, since it is smaller than the sum of its proper divisors (96327).

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

It is a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (93366).

90405 is a wasteful number, since it uses less digits than its factorization.

90405 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 66 (or 56 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 90405 is about 300.6742423288. The cubic root of 90405 is about 44.8811679565.

It can be divided in two parts, 9040 and 5, that added together give a triangular number (9045 = T₁₃₄).

The spelling of 90405 in words is "ninety thousand, four hundred five".