413414013012 has 192 divisors, whose sum is σ = 1296429625344. Its totient is φ = 99023938560.

The previous prime is 413414012989. The next prime is 413414013029. The reversal of 413414013012 is 210310414314.

It is a super-2 number, since 2×413414013012² (a number of 24 digits) contains 22 as substring.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 63 ways as a sum of consecutive naturals, for example, 12752568 + ... + 12784944.

It is an arithmetic number, because the mean of its divisors is an integer number (6752237632).

Almost surely, 2^413414013012 is an apocalyptic number.

413414013012 is a gapful number since it is divisible by the number (42) 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 413414013012, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (648214812672).

413414013012 is an abundant number, since it is smaller than the sum of its proper divisors (883015612332).

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

413414013012 is a wasteful number, since it uses less digits than its factorization.

413414013012 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 33478 (or 33476 counting only the distinct ones).

The product of its (nonzero) digits is 1152, while the sum is 24.

Adding to 413414013012 its reverse (210310414314), we get a palindrome (623724427326).

The spelling of 413414013012 in words is "four hundred thirteen billion, four hundred fourteen million, thirteen thousand, twelve".