311616 has 42 divisors (see below), whose sum is σ = 894842. Its totient is φ = 103680.

The previous prime is 311609. The next prime is 311653. The reversal of 311616 is 616113.

It can be written as a sum of positive squares in only one way, i.e., 254016 + 57600 = 504^2 + 240^2 .

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a nude number because it is divisible by every one of its digits.

It is a congruent number.

It is an unprimeable number.

311616 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 (5) of ones.

It is a polite number, since it can be written in 5 ways as a sum of consecutive naturals, for example, 306 + ... + 846.

2³¹¹⁶¹⁶ is an apocalyptic number.

311616 is a gapful number since it is divisible by the number (36) 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 311616, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (447421).

311616 is an abundant number, since it is smaller than the sum of its proper divisors (583226).

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

311616 is a wasteful number, since it uses less digits than its factorization.

311616 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 559 (or 546 counting only the distinct ones).

The product of its digits is 108, while the sum is 18.

The square root of 311616 is about 558.2257607814. The cubic root of 311616 is about 67.7963921123.

Adding to 311616 its reverse (616113), we get a palindrome (927729).

It can be divided in two parts, 31161 and 6, that multiplied together give a triangular number (186966 = T₆₁₁).

The spelling of 311616 in words is "three hundred eleven thousand, six hundred sixteen".