413013342331040 has 384 divisors, whose sum is σ = 1118858991667200. Its totient is φ = 142607316234240.

The previous prime is 413013342331021. The next prime is 413013342331043. The reversal of 413013342331040 is 40133243310314.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (32).

It is a junction number, because it is equal to n+sod(n) for n = 413013342330988 and 413013342331006.

It is not an unprimeable number, because it can be changed into a prime (413013342331043) by changing a digit.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 5667851726 + ... + 5667924594.

It is an arithmetic number, because the mean of its divisors is an integer number (2913695290800).

Almost surely, 2^{413013342331040} is an apocalyptic number.

413013342331040 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 413013342331040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (559429495833600).

413013342331040 is an abundant number, since it is smaller than the sum of its proper divisors (705845649336160).

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

413013342331040 is a wasteful number, since it uses less digits than its factorization.

413013342331040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 73940 (or 73932 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 32.

Adding to 413013342331040 its reverse (40133243310314), we get a palindrome (453146585641354).

The spelling of 413013342331040 in words is "four hundred thirteen trillion, thirteen billion, three hundred forty-two million, three hundred thirty-one thousand, forty".