205955414397216 has 768 divisors, whose sum is σ = 679396273920000. Its totient is φ = 60154936934400.

The previous prime is 205955414397197. The next prime is 205955414397247. The reversal of 205955414397216 is 612793414559502.

205955414397216 is a `hidden beast` number, since 2 + 0 + 5 + 9 + 5 + 541 + 4 + 3 + 9 + 72 + 16 = 666.

It is a super-3 number, since 3×205955414397216³ (a number of 44 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is an unprimeable number.

It is a polite number, since it can be written in 127 ways as a sum of consecutive naturals, for example, 81116743275 + ... + 81116745813.

It is an arithmetic number, because the mean of its divisors is an integer number (884630565000).

Almost surely, 2^{205955414397216} 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 205955414397216, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (339698136960000).

205955414397216 is an abundant number, since it is smaller than the sum of its proper divisors (473440859522784).

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

205955414397216 is a wasteful number, since it uses less digits than its factorization.

205955414397216 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5038 (or 5024 counting only the distinct ones).

The product of its (nonzero) digits is 81648000, while the sum is 63.

The spelling of 205955414397216 in words is "two hundred five trillion, nine hundred fifty-five billion, four hundred fourteen million, three hundred ninety-seven thousand, two hundred sixteen".