409 has 2 divisors, whose sum is σ = 410. Its totient is φ = 408.

The previous prime is 401. The next prime is 419. The reversal of 409 is 904.

409 = T_{15} + T_{16} +
T_{17}.

It is a happy number.

409 is nontrivially palindromic in base 4.

409 is an esthetic number in base 4, because in such base its adjacent digits differ by 1.

It is a weak prime.

It can be written as a sum of positive squares in only one way, i.e., 400 + 9 = 20^2 + 3^2 .

It is a cyclic number.

It is not a de Polignac number, because 409 - 2^{3} = 401 is a prime.

It is a Chen prime.

It is an Ulam number.

409 is an undulating number in base 4.

409 is a modest number, since divided by 9 gives 4 as remainder.

409 is a lucky number.

It is a plaindrome in base 7, base 13 and base 16.

It is a nialpdrome in base 8.

It is not a weakly prime, because it can be changed into another prime (401) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written as a sum of consecutive naturals, namely, 204 + 205.

It is an arithmetic number, because the mean of its divisors is an integer number (205).

409 is the 17-th centered triangular number.

It is an amenable number.

409 is a deficient number, since it is larger than the sum of its proper divisors (1).

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

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

The product of its (nonzero) digits is 36, while the sum is 13.

The square root of 409 is about 20.2237484162. The cubic root of 409 is about 7.4229141204.

Subtracting from 409 its product of nonzero digits (36), we obtain a palindrome (373).

It can be divided in two parts, 40 and 9, that added together give a square (49 = 7^{2}).

The spelling of 409 in words is "four hundred nine", and thus it is an aban number.

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