1413 has 6 divisors (see below), whose sum is σ = 2054. Its totient is φ = 936.

The previous prime is 1409. The next prime is 1423. The reversal of 1413 is 3141.

1413 is nontrivially palindromic in base 12 and base 16.

It can be written as a sum of positive squares in only one way, i.e., 1089 + 324 = 33^2 + 18^2 .

It is not a de Polignac number, because 1413 - 2² = 1409 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (9), and also a Moran number because the ratio is a prime number: 157 = 1413 / (1 + 4 + 1 + 3).

It is a Duffinian number.

1413 is an undulating number in base 16.

1413 is a nontrivial repdigit in base 12.

It is a plaindrome in base 12.

It is a nialpdrome in base 12 and base 15.

It is a zygodrome in base 12.

It is a junction number, because it is equal to n+sod(n) for n = 1395 and 1404.

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (1423) 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 5 ways as a sum of consecutive naturals, for example, 70 + ... + 87.

2¹⁴¹³ is an apocalyptic number.

It is an amenable number.

1413 is a deficient number, since it is larger than the sum of its proper divisors (641).

1413 is a wasteful number, since it uses less digits than its factorization.

1413 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 163 (or 160 counting only the distinct ones).

The product of its digits is 12, while the sum is 9.

The square root of 1413 is about 37.5898922584. The cubic root of 1413 is about 11.2214088806.

Adding to 1413 its reverse (3141), we get a palindrome (4554).

Subtracting 1413 from its reverse (3141), we obtain a cube (1728 = 12³).

It can be divided in two parts, 141 and 3, that added together give a square (144 = 12²).

The spelling of 1413 in words is "one thousand, four hundred thirteen".