• 405 can be written using four 4's:

405 has 10 divisors (see below), whose sum is σ = 726. Its totient is φ = 216.

The previous prime is 401. The next prime is 409. The reversal of 405 is 504.

405 is nontrivially palindromic in base 13.

It is an interprime number because it is at equal distance from previous prime (401) and next prime (409).

It can be written as a sum of positive squares in only one way, i.e., 324 + 81 = 18^2 + 9^2 .

It is not a de Polignac number, because 405 - 2^{2} = 401 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9).

405 is an undulating number in base 13.

It is a Curzon number.

It is a plaindrome in base 7, base 11 and base 12.

It is a nialpdrome in base 5 and base 9.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a 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 in 9 ways as a sum of consecutive naturals, for example, 79 + ... + 83.

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

It is an amenable number.

405 is a deficient number, since it is larger than the sum of its proper divisors (321).

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

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

The sum of its prime factors is 17 (or 8 counting only the distinct ones).

The product of its (nonzero) digits is 20, while the sum is 9.

The square root of 405 is about 20.1246117975. The cubic root of 405 is about 7.3986362230.

Multiplying 405 by its product of nonzero digits (20), we get a square (8100 = 90^{2}).

Adding to 405 its reverse (504), we get a palindrome (909).

Subtracting 405 from its reverse (504), we obtain a palindrome (99).

It can be divided in two parts, 40 and 5, that added together give a triangular number (45 = T_{9}).

The spelling of 405 in words is "four hundred five", and thus it is an aban number.

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