413414101414314 has 384 divisors, whose sum is σ = 1213456245281280. Its totient is φ = 99050154255360.

The previous prime is 413414101414309. The next prime is 413414101414333.

413414101414314 is a `hidden beast` number, since 4 + 1 + 3 + 41 + 41 + 0 + 141 + 431 + 4 = 666.

413414101414314 is nontrivially palindromic in base 10.

It is a super-2 number, since 2×413414101414314² (a number of 30 digits) contains 22 as substring.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (31) of ones.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 3115408014 + ... + 3115540710.

It is an arithmetic number, because the mean of its divisors is an integer number (3160042305420).

Almost surely, 2^{413414101414314} is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413414101414314, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (606728122640640).

413414101414314 is an abundant number, since it is smaller than the sum of its proper divisors (800042143866966).

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

413414101414314 is a wasteful number, since it uses less digits than its factorization.

413414101414314 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 134187 (or 134162 counting only the distinct ones).

The product of its (nonzero) digits is 36864, while the sum is 36.

It can be divided in two parts, 41341410 and 1414314, that added together give a palindrome (42755724).

The spelling of 413414101414314 in words is "four hundred thirteen trillion, four hundred fourteen billion, one hundred one million, four hundred fourteen thousand, three hundred fourteen".