413871120 has 400 divisors, whose sum is σ = 1644738480. Its totient is φ = 95883264.

The previous prime is 413871119. The next prime is 413871121. The reversal of 413871120 is 21178314.

It is an interprime number because it is at equal distance from previous prime (413871119) and next prime (413871121).

It can be written as a sum of positive squares in 8 ways, for example, as 18974736 + 394896384 = 4356^2 + 19872^2 .

It is a Harshad number since it is a multiple of its sum of digits (27).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (413871121) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (11) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 24345352 + ... + 24345368.

Almost surely, 2^413871120 is an apocalyptic number.

413871120 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 413871120, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (822369240).

413871120 is an abundant number, since it is smaller than the sum of its proper divisors (1230867360).

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

413871120 is a wasteful number, since it uses less digits than its factorization.

413871120 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 89 (or 40 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 27.

The square root of 413871120 is about 20343.8226496399. The cubic root of 413871120 is about 745.2266445544.

The spelling of 413871120 in words is "four hundred thirteen million, eight hundred seventy-one thousand, one hundred twenty".