101114517667968 has 768 divisors, whose sum is σ = 351618029568000. Its totient is φ = 27282653798400.

The previous prime is 101114517667937. The next prime is 101114517667993. The reversal of 101114517667968 is 869766715411101.

It is a happy number.

101114517667968 is a `hidden beast` number, since 1 + 0 + 11 + 14 + 517 + 6 + 6 + 7 + 96 + 8 = 666.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 1976759193 + ... + 1976810343.

It is an arithmetic number, because the mean of its divisors is an integer number (457835976000).

Almost surely, 2^{101114517667968} is an apocalyptic number.

101114517667968 is a gapful number since it is divisible by the number (18) 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 101114517667968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (175809014784000).

101114517667968 is an abundant number, since it is smaller than the sum of its proper divisors (250503511900032).

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

101114517667968 is a wasteful number, since it uses less digits than its factorization.

101114517667968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 51393 (or 51378 counting only the distinct ones).

The product of its (nonzero) digits is 15240960, while the sum is 63.

The spelling of 101114517667968 in words is "one hundred one trillion, one hundred fourteen billion, five hundred seventeen million, six hundred sixty-seven thousand, nine hundred sixty-eight".