513416414016 has 168 divisors, whose sum is σ = 1610533963584. Its totient is φ = 155083069440.

The previous prime is 513416413981. The next prime is 513416414111. The reversal of 513416414016 is 610414614315.

513416414016 is a `hidden beast` number, since 5 + 1 + 3 + 4 + 1 + 641 + 4 + 0 + 1 + 6 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1853725 + ... + 2112611.

It is an arithmetic number, because the mean of its divisors is an integer number (9586511688).

Almost surely, 2^513416414016 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 513416414016, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (805266981792).

513416414016 is an abundant number, since it is smaller than the sum of its proper divisors (1097117549568).

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

513416414016 is a wasteful number, since it uses less digits than its factorization.

513416414016 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 259229 (or 259216 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 513416414016 in words is "five hundred thirteen billion, four hundred sixteen million, four hundred fourteen thousand, sixteen".