413663760 has 280 divisors, whose sum is σ = 1485701784. Its totient is φ = 106997760.

The previous prime is 413663749. The next prime is 413663797. The reversal of 413663760 is 67366314.

It is a happy number.

413663760 is a `hidden beast` number, since 4 + 13 + 6 + 637 + 6 + 0 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 31539456 + 382124304 = 5616^2 + 19548^2 .

It is a super-2 number, since 2×413663760² = 342235412674675200, which contains 22 as substring.

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

It is an unprimeable number.

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 55 ways as a sum of consecutive naturals, for example, 2391034 + ... + 2391206.

Almost surely, 2^413663760 is an apocalyptic number.

413663760 is a gapful number since it is divisible by the number (40) 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 413663760, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (742850892).

413663760 is an abundant number, since it is smaller than the sum of its proper divisors (1072038024).

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

413663760 is a wasteful number, since it uses less digits than its factorization.

413663760 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 245 (or 224 counting only the distinct ones).

The product of its (nonzero) digits is 54432, while the sum is 36.

The square root of 413663760 is about 20338.7256237946. The cubic root of 413663760 is about 745.1021645697.

It can be divided in two parts, 4136 and 63760, that added together give a triangular number (67896 = T₃₆₈).

The spelling of 413663760 in words is "four hundred thirteen million, six hundred sixty-three thousand, seven hundred sixty".