413514415314 has 192 divisors, whose sum is σ = 1209006489600. Its totient is φ = 98645247360.

The previous prime is 413514415261. The next prime is 413514415357.

413514415314 is a `hidden beast` number, since 41 + 3 + 514 + 41 + 53 + 14 = 666.

413514415314 is nontrivially palindromic in base 10.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 3527919 + ... + 3643245.

It is an arithmetic number, because the mean of its divisors is an integer number (6296908800).

Almost surely, 2^413514415314 is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413514415314, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (604503244800).

413514415314 is an abundant number, since it is smaller than the sum of its proper divisors (795492074286).

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

413514415314 is a wasteful number, since it uses less digits than its factorization.

413514415314 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 115565 (or 115562 counting only the distinct ones).

The product of its digits is 57600, while the sum is 36.

It can be divided in two parts, 413514 and 415314, that added together give a palindrome (828828).

The spelling of 413514415314 in words is "four hundred thirteen billion, five hundred fourteen million, four hundred fifteen thousand, three hundred fourteen".