101585664 has 216 divisors, whose sum is σ = 321414912. Its totient is φ = 31933440.

The previous prime is 101585657. The next prime is 101585677. The reversal of 101585664 is 466585101.

101585664 is a `hidden beast` number, since 10 + 1 + 585 + 6 + 64 = 666.

It is a tau number, because it is divible by the number of its divisors (216).

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

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 1430749 + ... + 1430819.

It is an arithmetic number, because the mean of its divisors is an integer number (1488032).

Almost surely, 2^101585664 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 101585664, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (160707456).

101585664 is an abundant number, since it is smaller than the sum of its proper divisors (219829248).

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

101585664 is an frugal number, since it uses more digits than its factorization.

101585664 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 125 (or 99 counting only the distinct ones).

The product of its (nonzero) digits is 28800, while the sum is 36.

The square root of 101585664 is about 10078.9713760879. The cubic root of 101585664 is about 466.5993626293.

The spelling of 101585664 in words is "one hundred one million, five hundred eighty-five thousand, six hundred sixty-four".