413152014400 has 168 divisors, whose sum is σ = 1042617158856. Its totient is φ = 161042841600.

The previous prime is 413152014391. The next prime is 413152014427. The reversal of 413152014400 is 4410251314.

It can be written as a sum of positive squares in 12 ways, for example, as 130153549824 + 282998464576 = 360768^2 + 531976^2 .

It is a Harshad number since it is a multiple of its sum of digits (25).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 65400042 + ... + 65406358.

It is an arithmetic number, because the mean of its divisors is an integer number (6206054517).

Almost surely, 2^413152014400 is an apocalyptic number.

413152014400 is a gapful number since it is divisible by the number (40) 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 413152014400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (521308579428).

413152014400 is an abundant number, since it is smaller than the sum of its proper divisors (629465144456).

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

413152014400 is a wasteful number, since it uses less digits than its factorization.

413152014400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 7377 (or 7362 counting only the distinct ones).

The product of its (nonzero) digits is 1920, while the sum is 25.

Adding to 413152014400 its reverse (4410251314), we get a palindrome (417562265714).

The spelling of 413152014400 in words is "four hundred thirteen billion, one hundred fifty-two million, fourteen thousand, four hundred".