101617104960 has 560 divisors, whose sum is σ = 415956414720. Its totient is φ = 23066726400.

The previous prime is 101617104947. The next prime is 101617105013. The reversal of 101617104960 is 69401716101.

101617104960 is a `hidden beast` number, since 1 + 0 + 161 + 7 + 1 + 0 + 496 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (560).

It is a super-4 number, since 4×101617104960⁴ (a number of 45 digits) contains 4444 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 27395586 + ... + 27399294.

It is an arithmetic number, because the mean of its divisors is an integer number (742779312).

Almost surely, 2^101617104960 is an apocalyptic number.

101617104960 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 101617104960, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (207978207360).

101617104960 is an abundant number, since it is smaller than the sum of its proper divisors (314339309760).

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

101617104960 is a wasteful number, since it uses less digits than its factorization.

101617104960 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 3896 (or 3877 counting only the distinct ones).

The product of its (nonzero) digits is 9072, while the sum is 36.

The spelling of 101617104960 in words is "one hundred one billion, six hundred seventeen million, one hundred four thousand, nine hundred sixty".