413149040640 has 1040 divisors, whose sum is σ = 1730907965952. Its totient is φ = 92302737408.

The previous prime is 413149040611. The next prime is 413149040651. The reversal of 413149040640 is 46040941314.

It is a happy number.

413149040640 is a `hidden beast` number, since 4 + 1 + 3 + 1 + 4 + 9 + 0 + 4 + 0 + 640 = 666.

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

It is a junction number, because it is equal to n+sod(n) for n = 413149040595 and 413149040604.

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 545771142 + ... + 545771898.

Almost surely, 2^413149040640 is an apocalyptic number.

413149040640 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 413149040640, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (865453982976).

413149040640 is an abundant number, since it is smaller than the sum of its proper divisors (1317758925312).

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

413149040640 is an equidigital number, since it uses as much as digits as its factorization.

413149040640 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 852 (or 821 counting only the distinct ones).

The product of its (nonzero) digits is 41472, while the sum is 36.

Adding to 413149040640 its reverse (46040941314), we get a palindrome (459189981954).

The spelling of 413149040640 in words is "four hundred thirteen billion, one hundred forty-nine million, forty thousand, six hundred forty".