101516400 has 180 divisors, whose sum is σ = 356500248. Its totient is φ = 26749440.

The previous prime is 101516399. The next prime is 101516407. The reversal of 101516400 is 4615101.

101516400 is a `hidden beast` number, since 10 + 15 + 1 + 640 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (180).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (101516407) by changing a digit.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 586714 + ... + 586886.

Almost surely, 2^101516400 is an apocalyptic number.

101516400 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 101516400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (178250124).

101516400 is an abundant number, since it is smaller than the sum of its proper divisors (254983848).

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

101516400 is a wasteful number, since it uses less digits than its factorization.

101516400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 360 (or 346 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 18.

The square root of 101516400 is about 10075.5347252640. The cubic root of 101516400 is about 466.4932916051.

The spelling of 101516400 in words is "one hundred one million, five hundred sixteen thousand, four hundred".