409513 has 12 divisors (see below), whose sum is σ = 472780. Its totient is φ = 352512.

The previous prime is 409499. The next prime is 409517. The reversal of 409513 is 315904.

409513 = 452² + 453².

It can be written as a sum of positive squares in 6 ways, for example, as 16384 + 393129 = 128^2 + 627^2 .

It is not a de Polignac number, because 409513 - 2¹³ = 401321 is a prime.

It is a hoax number, since the sum of its digits (22) coincides with the sum of the digits of its distinct prime factors.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (409517) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 3703 + ... + 3811.

2⁴⁰⁹⁵¹³ is an apocalyptic number.

409513 is the 453-rd centered square number.

It is an amenable number.

409513 is a deficient number, since it is larger than the sum of its proper divisors (63267).

409513 is a wasteful number, since it uses less digits than its factorization.

409513 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 156 (or 139 counting only the distinct ones).

The product of its (nonzero) digits is 540, while the sum is 22.

The square root of 409513 is about 639.9320276404. The cubic root of 409513 is about 74.2601629156.

It can be divided in two parts, 4095 and 13, that multiplied together give a palindrome (53235).

The spelling of 409513 in words is "four hundred nine thousand, five hundred thirteen".