101954417160960 has 6912 divisors, whose sum is σ = 499478773248000. Its totient is φ = 19720680505344.

The previous prime is 101954417160949. The next prime is 101954417160983. The reversal of 101954417160960 is 69061714459101.

101954417160960 is a `hidden beast` number, since 1 + 0 + 1 + 9 + 5 + 4 + 417 + 160 + 9 + 60 = 666.

It is a tau number, because it is divible by the number of its divisors (6912).

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a junction number, because it is equal to n+sod(n) for n = 101954417160897 and 101954417160906.

It is an unprimeable number.

It is a polite number, since it can be written in 767 ways as a sum of consecutive naturals, for example, 1396635851484 + ... + 1396635851556.

It is an arithmetic number, because the mean of its divisors is an integer number (72262554000).

Almost surely, 2^{101954417160960} is an apocalyptic number.

101954417160960 is a gapful number since it is divisible by the number (10) 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 101954417160960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (249739386624000).

101954417160960 is an abundant number, since it is smaller than the sum of its proper divisors (397524356087040).

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

101954417160960 is an equidigital number, since it uses as much as digits as its factorization.

101954417160960 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 215 (or 175 counting only the distinct ones).

The product of its (nonzero) digits is 1632960, while the sum is 54.

The spelling of 101954417160960 in words is "one hundred one trillion, nine hundred fifty-four billion, four hundred seventeen million, one hundred sixty thousand, nine hundred sixty".