409005 has 24 divisors (see below), whose sum is σ = 725400. Its totient is φ = 213120.

The previous prime is 408997. The next prime is 409007. The reversal of 409005 is 500904.

It can be written as a sum of positive squares in 4 ways, for example, as 15876 + 393129 = 126^2 + 627^2 .

It is not a de Polignac number, because 409005 - 2³ = 408997 is a prime.

It is a Curzon number.

409005 is a lucky number.

It is a congruent number.

It is an inconsummate number, since it does not exist a number n which divided by its sum of digits gives 409005.

It is not an unprimeable number, because it can be changed into a prime (409007) by changing a digit.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 2671 + ... + 2819.

It is an arithmetic number, because the mean of its divisors is an integer number (30225).

2⁴⁰⁹⁰⁰⁵ is an apocalyptic number.

409005 is a gapful number since it is divisible by the number (45) formed by its first and last digit.

It is an amenable number.

409005 is a deficient number, since it is larger than the sum of its proper divisors (316395).

409005 is a wasteful number, since it uses less digits than its factorization.

409005 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 221 (or 218 counting only the distinct ones).

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

The square root of 409005 is about 639.5349873150. The cubic root of 409005 is about 74.2294436854.

Adding to 409005 its reverse (500904), we get a palindrome (909909).

It can be divided in two parts, 40 and 9005, that added together give a triangular number (9045 = T₁₃₄).

The spelling of 409005 in words is "four hundred nine thousand, five".