13120416400 has 540 divisors, whose sum is σ = 42221892492. Its totient is φ = 3891363840.

The previous prime is 13120416377. The next prime is 13120416433. The reversal of 13120416400 is 461402131.

It can be written as a sum of positive squares in 18 ways, for example, as 12368998656 + 751417744 = 111216^2 + 27412^2 .

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (13) of ones.

It is a polite number, since it can be written in 107 ways as a sum of consecutive naturals, for example, 56310684 + ... + 56310916.

Almost surely, 2^13120416400 is an apocalyptic number.

13120416400 is a gapful number since it is divisible by the number (10) 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 13120416400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (21110946246).

13120416400 is an abundant number, since it is smaller than the sum of its proper divisors (29101476092).

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

13120416400 is a wasteful number, since it uses less digits than its factorization.

13120416400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 308 (or 277 counting only the distinct ones).

The product of its (nonzero) digits is 576, while the sum is 22.

Adding to 13120416400 its reverse (461402131), we get a palindrome (13581818531).

The spelling of 13120416400 in words is "thirteen billion, one hundred twenty million, four hundred sixteen thousand, four hundred".