101953609395264 has 1575 divisors, whose sum is σ = 356706593762805. Its totient is φ = 28789159449600.

The previous prime is 101953609395241. The next prime is 101953609395289. The reversal of 101953609395264 is 462593906359101.

The square root of 101953609395264 is 10097208.

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

101953609395264 is a `hidden beast` number, since 1 + 0 + 1 + 9 + 5 + 360 + 9 + 3 + 9 + 5 + 264 = 666.

It can be written as a sum of positive squares in only one way, i.e., 3315341772864 + 98638267622400 = 1820808^2 + 9931680^2 .

It is an unprimeable number.

It is a polite number, since it can be written in 224 ways as a sum of consecutive naturals, for example, 1671370645794 + ... + 1671370645854.

Almost surely, 2^{101953609395264} is an apocalyptic number.

101953609395264 is the 10097208-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 101953609395264

101953609395264 is an abundant number, since it is smaller than the sum of its proper divisors (254752984367541).

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

101953609395264 is an frugal number, since it uses more digits than its factorization.

101953609395264 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 228 (or 96 counting only the distinct ones).

The product of its (nonzero) digits is 47239200, while the sum is 63.

The spelling of 101953609395264 in words is "one hundred one trillion, nine hundred fifty-three billion, six hundred nine million, three hundred ninety-five thousand, two hundred sixty-four".