1313728416 has 768 divisors, whose sum is σ = 5419008000. Its totient is φ = 304819200.

The previous prime is 1313728393. The next prime is 1313728439. The reversal of 1313728416 is 6148273131.

It is a happy number.

1313728416 is digitally balanced in base 4, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (1313728393) and next prime (1313728439).

It is a Harshad number since it is a multiple of its sum of digits (36).

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

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 42378321 + ... + 42378351.

It is an arithmetic number, because the mean of its divisors is an integer number (7056000).

Almost surely, 2^1313728416 is an apocalyptic number.

1313728416 is a gapful number since it is divisible by the number (16) 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 1313728416, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2709504000).

1313728416 is an abundant number, since it is smaller than the sum of its proper divisors (4105279584).

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

1313728416 is a wasteful number, since it uses less digits than its factorization.

1313728416 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 95 (or 67 counting only the distinct ones).

The product of its digits is 24192, while the sum is 36.

The square root of 1313728416 is about 36245.3916519052. The cubic root of 1313728416 is about 1095.2212575974.

The spelling of 1313728416 in words is "one billion, three hundred thirteen million, seven hundred twenty-eight thousand, four hundred sixteen".