513361 has 8 divisors (see below), whose sum is σ = 554400. Its totient is φ = 473760.

The previous prime is 513353. The next prime is 513367. The reversal of 513361 is 163315.

513361 = 35² + 36² + ... + 116².

It is a sphenic number, since it is the product of 3 distinct primes.

It is a cyclic number.

It is not a de Polignac number, because 513361 - 2³ = 513353 is a prime.

It is a Harshad number since it is a multiple of its sum of digits (19).

It is a Duffinian number.

513361 is a lucky number.

It is not an unprimeable number, because it can be changed into a prime (513367) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 450 + ... + 1108.

It is an arithmetic number, because the mean of its divisors is an integer number (69300).

2⁵¹³³⁶¹ is an apocalyptic number.

It is an amenable number.

513361 is a deficient number, since it is larger than the sum of its proper divisors (41039).

513361 is a wasteful number, since it uses less digits than its factorization.

513361 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 719.

The product of its digits is 270, while the sum is 19.

The square root of 513361 is about 716.4921492940. The cubic root of 513361 is about 80.0708227000.

Adding to 513361 its reverse (163315), we get a palindrome (676676).

It can be divided in two parts, 513 and 361, that multiplied together give a cube (185193 = 57³).

The spelling of 513361 in words is "five hundred thirteen thousand, three hundred sixty-one".