9505085760 has 336 divisors, whose sum is σ = 33864968592. Its totient is φ = 2445312000.

The previous prime is 9505085743. The next prime is 9505085767. The reversal of 9505085760 is 675805059.

9505085760 is a `hidden beast` number, since 9 + 505 + 0 + 85 + 7 + 60 = 666.

It can be written as a sum of positive squares in 8 ways, for example, as 43243776 + 9461841984 = 6576^2 + 97272^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (9505085767) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 11925682 + ... + 11926478.

It is an arithmetic number, because the mean of its divisors is an integer number (100788597).

Almost surely, 2^9505085760 is an apocalyptic number.

9505085760 is a gapful number since it is divisible by the number (90) 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 9505085760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (16932484296).

9505085760 is an abundant number, since it is smaller than the sum of its proper divisors (24359882832).

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

9505085760 is a wasteful number, since it uses less digits than its factorization.

9505085760 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 962 (or 949 counting only the distinct ones).

The product of its (nonzero) digits is 378000, while the sum is 45.

The square root of 9505085760 is about 97494.0293556482. The cubic root of 9505085760 is about 2118.2896612346.

The spelling of 9505085760 in words is "nine billion, five hundred five million, eighty-five thousand, seven hundred sixty".