165409517418912 has 1152 divisors, whose sum is σ = 531958184896320. Its totient is φ = 48428042158080.

The previous prime is 165409517418889. The next prime is 165409517418989. The reversal of 165409517418912 is 219814715904561.

165409517418912 is a `hidden beast` number, since 1 + 6 + 5 + 40 + 95 + 1 + 7 + 418 + 91 + 2 = 666.

It can be written as a sum of positive squares in 32 ways, for example, as 2598144239376 + 162811373179536 = 1611876^2 + 12759756^2 .

It is a self number, because there is not a number n which added to its sum of digits gives 165409517418912.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 404424247764 + ... + 404424248172.

Almost surely, 2^{165409517418912} is an apocalyptic number.

165409517418912 is a gapful number since it is divisible by the number (12) 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 165409517418912, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (265979092448160).

165409517418912 is an abundant number, since it is smaller than the sum of its proper divisors (366548667477408).

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

165409517418912 is a wasteful number, since it uses less digits than its factorization.

165409517418912 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 906 (or 895 counting only the distinct ones).

The product of its (nonzero) digits is 21772800, while the sum is 63.

The spelling of 165409517418912 in words is "one hundred sixty-five trillion, four hundred nine billion, five hundred seventeen million, four hundred eighteen thousand, nine hundred twelve".