413163648 has 192 divisors, whose sum is σ = 1280518200. Its totient is φ = 127844352.

The previous prime is 413163637. The next prime is 413163649. The reversal of 413163648 is 846361314.

It is a happy number.

413163648 is a `hidden beast` number, since 4 + 1 + 3 + 1 + 6 + 3 + 648 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 375119424 + 38044224 = 19368^2 + 6168^2 .

It is a tau number, because it is divible by the number of its divisors (192).

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

It is a nude number because it is divisible by every one of its digits.

Its product of digits (41472) is a multiple of the sum of its prime factors (144).

It is not an unprimeable number, because it can be changed into a prime (413163649) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (7) of ones.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 5659740 + ... + 5659812.

Almost surely, 2^413163648 is an apocalyptic number.

413163648 is a gapful number since it is divisible by the number (48) 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 413163648, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (640259100).

413163648 is an abundant number, since it is smaller than the sum of its proper divisors (867354552).

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

413163648 is an equidigital number, since it uses as much as digits as its factorization.

413163648 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 144 (or 95 counting only the distinct ones).

The product of its digits is 41472, while the sum is 36.

The square root of 413163648 is about 20326.4273299564. The cubic root of 413163648 is about 744.8017718029.

The spelling of 413163648 in words is "four hundred thirteen million, one hundred sixty-three thousand, six hundred forty-eight".