86409 has 6 divisors (see below), whose sum is σ = 124826. Its totient is φ = 57600.

The previous prime is 86399. The next prime is 86413. The reversal of 86409 is 90468.

It can be written as a sum of positive squares in only one way, i.e., 81225 + 5184 = 285^2 + 72^2 .

It is not a de Polignac number, because 86409 - 2¹⁶ = 20873 is a prime.

It is a Duffinian number.

86409 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 86409.

It is not an unprimeable number, because it can be changed into a prime (86209) 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 5 ways as a sum of consecutive naturals, for example, 4792 + ... + 4809.

2⁸⁶⁴⁰⁹ is an apocalyptic number.

It is an amenable number.

86409 is a deficient number, since it is larger than the sum of its proper divisors (38417).

86409 is a wasteful number, since it uses less digits than its factorization.

86409 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 9607 (or 9604 counting only the distinct ones).

The product of its (nonzero) digits is 1728, while the sum is 27.

The square root of 86409 is about 293.9540780462. The cubic root of 86409 is about 44.2099129435.

Adding to 86409 its sum of digits (27), we get a square (86436 = 294²).

Subtracting from 86409 its product of nonzero digits (1728), we obtain a square (84681 = 291²).

It can be divided in two parts, 8640 and 9, that added together give a square (8649 = 93²).

The spelling of 86409 in words is "eighty-six thousand, four hundred nine".