413122505221314 has 96 divisors (see below), whose sum is σ = 1056087477080064. Its totient is φ = 114214609703520.

The previous prime is 413122505221247. The next prime is 413122505221337.

413122505221314 is a `hidden beast` number, since 4 + 1 + 3 + 12 + 2 + 505 + 2 + 2 + 131 + 4 = 666.

413122505221314 is nontrivially palindromic in base 10.

It is a super-2 number, since 2×413122505221314² (a number of 30 digits) contains 22 as substring.

It is an unprimeable number.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 28926637 + ... + 40779839.

It is an arithmetic number, because the mean of its divisors is an integer number (11000911219584).

Almost surely, 2^{413122505221314} is an apocalyptic number.

It is a practical number, because each smaller number is the sum of distinct divisors of 413122505221314, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (528043738540032).

413122505221314 is an abundant number, since it is smaller than the sum of its proper divisors (642964971858750).

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

413122505221314 is a wasteful number, since it uses less digits than its factorization.

413122505221314 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 11862172 (or 11862169 counting only the distinct ones).

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

It can be divided in two parts, 41312250 and 5221314, that added together give a palindrome (46533564).

The spelling of 413122505221314 in words is "four hundred thirteen trillion, one hundred twenty-two billion, five hundred five million, two hundred twenty-one thousand, three hundred fourteen".