13530585600 has 1440 divisors, whose sum is σ = 62472072960. Its totient is φ = 2848849920.

The previous prime is 13530585599. The next prime is 13530585637. The reversal of 13530585600 is 658503531.

13530585600 is a `hidden beast` number, since 13 + 5 + 3 + 0 + 585 + 60 + 0 = 666.

It is a tau number, because it is divible by the number of its divisors (1440).

It is a hoax number, since the sum of its digits (36) coincides with the sum of the digits of its distinct prime factors.

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 143 ways as a sum of consecutive naturals, for example, 287884777 + ... + 287884823.

It is an arithmetic number, because the mean of its divisors is an integer number (43383384).

Almost surely, 2^13530585600 is an apocalyptic number.

13530585600 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 13530585600, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (31236036480).

13530585600 is an abundant number, since it is smaller than the sum of its proper divisors (48941487360).

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

13530585600 is a wasteful number, since it uses less digits than its factorization.

13530585600 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 115 (or 81 counting only the distinct ones).

The product of its (nonzero) digits is 54000, while the sum is 36.

The spelling of 13530585600 in words is "thirteen billion, five hundred thirty million, five hundred eighty-five thousand, six hundred".