9504 has 48 divisors (see below), whose sum is σ = 30240. Its totient is φ = 2880.

The previous prime is 9497. The next prime is 9511. The reversal of 9504 is 4059.

It is an interprime number because it is at equal distance from previous prime (9497) and next prime (9511).

It is a tau number, because it is divible by the number of its divisors (48).

Together with 20735 it forms a betrothed pair.

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

It is a plaindrome in base 14.

It is a nialpdrome in base 13.

It is an unprimeable number.

9504 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 859 + ... + 869.

It is an arithmetic number, because the mean of its divisors is an integer number (630).

2⁹⁵⁰⁴ 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 9504, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (15120).

9504 is an abundant number, since it is smaller than the sum of its proper divisors (20736).

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

9504 is a wasteful number, since it uses less digits than its factorization.

9504 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 30 (or 16 counting only the distinct ones).

The product of its (nonzero) digits is 180, while the sum is 18.

The square root of 9504 is about 97.4884608556. The cubic root of 9504 is about 21.1820900120.

9504 divided by its sum of digits (18) gives a triangular number (528 = T₃₂).

Subtracting from 9504 its reverse (4059), we obtain a palindrome (5445).

The spelling of 9504 in words is "nine thousand, five hundred four".