205117920 has 720 divisors, whose sum is σ = 938543760. Its totient is φ = 41803776.

The previous prime is 205117909. The next prime is 205117931. The reversal of 205117920 is 29711502.

205117920 is digitally balanced in base 2, because in such base it contains all the possibile digits an equal number of times.

It is an interprime number because it is at equal distance from previous prime (205117909) and next prime (205117931).

It is a tau number, because it is divible by the number of its divisors (720).

It is a super-2 number, since 2×205117920² = 84146722210252800, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 119 ways as a sum of consecutive naturals, for example, 10795671 + ... + 10795689.

It is an arithmetic number, because the mean of its divisors is an integer number (1303533).

Almost surely, 2^205117920 is an apocalyptic number.

205117920 is a gapful number since it is divisible by the number (20) 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 205117920, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (469271880).

205117920 is an abundant number, since it is smaller than the sum of its proper divisors (733425840).

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

205117920 is a wasteful number, since it uses less digits than its factorization.

205117920 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 77 (or 53 counting only the distinct ones).

The product of its (nonzero) digits is 1260, while the sum is 27.

The square root of 205117920 is about 14321.9384162899. The cubic root of 205117920 is about 589.7498892010.

The spelling of 205117920 in words is "two hundred five million, one hundred seventeen thousand, nine hundred twenty".