61504 has 21 divisors (see below), whose sum is σ = 126111. Its totient is φ = 29760.

The previous prime is 61493. The next prime is 61507. The reversal of 61504 is 40516.

61504 = T₂₄₇ + T₂₄₈.

The square root of 61504 is 248.

It is a perfect power (a square), and thus also a powerful number.

It is a Harshad number since it is a multiple of its sum of digits (16).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (61507) by changing a digit.

61504 is an untouchable number, because it is not equal to the sum of proper divisors of any number.

It is a pernicious number, because its binary representation contains a prime number (5) of ones.

It is a polite number, since it can be written in 2 ways as a sum of consecutive naturals, for example, 1969 + ... + 1999.

2⁶¹⁵⁰⁴ is an apocalyptic number.

61504 is a gapful number since it is divisible by the number (64) formed by its first and last digit.

61504 is the 248-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 61504

61504 is an abundant number, since it is smaller than the sum of its proper divisors (64607).

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

61504 is an equidigital number, since it uses as much as digits as its factorization.

61504 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 74 (or 33 counting only the distinct ones).

The product of its (nonzero) digits is 120, while the sum is 16.

The cubic root of 61504 is about 39.4730896129.

Multiplying 61504 by its sum of digits (16), we get a square (984064 = 992²).

61504 divided by its sum of digits (16) gives a square (3844 = 62²).

It can be divided in two parts, 61 and 504, that added together give a palindrome (565).

The spelling of 61504 in words is "sixty-one thousand, five hundred four".