172688956007689 has 81 divisors (see below), whose sum is σ = 198823428325557. Its totient is φ = 149871811161600.

The previous prime is 172688956007657. The next prime is 172688956007699. The reversal of 172688956007689 is 986700659886271.

The square root of 172688956007689 is 13141117.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 84674687553225 + 88014268454464 = 9201885^2 + 9381592^2 .

It is not a de Polignac number, because 172688956007689 - 2⁵ = 172688956007657 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (172688956007629) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 398819759617 + ... + 398819760049.

Almost surely, 2^{172688956007689} is an apocalyptic number.

172688956007689 is the 13141117-th square number.

172688956007689 is the 6570559-th centered octagonal number.

It is an amenable number.

172688956007689 is a deficient number, since it is larger than the sum of its proper divisors (26134472317868).

172688956007689 is an frugal number, since it uses more digits than its factorization.

172688956007689 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1128 (or 564 counting only the distinct ones).

The product of its (nonzero) digits is 4389396480, while the sum is 82.

The spelling of 172688956007689 in words is "one hundred seventy-two trillion, six hundred eighty-eight billion, nine hundred fifty-six million, seven thousand, six hundred eighty-nine".