513648 has 80 divisors (see below), whose sum is σ = 1562400. Its totient is φ = 161280.

The previous prime is 513641. The next prime is 513649. The reversal of 513648 is 846315.

513648 is a `hidden beast` number, since 5 + 13 + 648 = 666.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (513641) by changing a digit.

513648 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

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 15 ways as a sum of consecutive naturals, for example, 12508 + ... + 12548.

It is an arithmetic number, because the mean of its divisors is an integer number (19530).

513648 is a Friedman number, since it can be written as 58*41*6^3, using all its digits and the basic arithmetic operations.

2⁵¹³⁶⁴⁸ is an apocalyptic number.

513648 is a gapful number since it is divisible by the number (58) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (781200).

513648 is an abundant number, since it is smaller than the sum of its proper divisors (1048752).

It is a pseudoperfect number, because it is the sum of a subset of its proper divisors.

513648 is a wasteful number, since it uses less digits than its factorization.

513648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 87 (or 75 counting only the distinct ones).

The product of its digits is 2880, while the sum is 27.

The square root of 513648 is about 716.6924026387. The cubic root of 513648 is about 80.0857414056.

It can be divided in two parts, 5136 and 48, that added together give a square (5184 = 72²).

The spelling of 513648 in words is "five hundred thirteen thousand, six hundred forty-eight".