413293440 has 384 divisors, whose sum is σ = 1607454720. Its totient is φ = 89886720.

The previous prime is 413293427. The next prime is 413293451. The reversal of 413293440 is 44392314.

It is a tau number, because it is divible by the number of its divisors (384).

It is a super-2 number, since 2×413293440² = 341622935094067200, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (30).

It is a junction number, because it is equal to n+sod(n) for n = 413293398 and 413293407.

It is a congruent number.

It is an unprimeable number.

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 47 ways as a sum of consecutive naturals, for example, 2163745 + ... + 2163935.

It is an arithmetic number, because the mean of its divisors is an integer number (4186080).

Almost surely, 2^413293440 is an apocalyptic number.

413293440 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 413293440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (803727360).

413293440 is an abundant number, since it is smaller than the sum of its proper divisors (1194161280).

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

413293440 is a wasteful number, since it uses less digits than its factorization.

413293440 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 250 (or 231 counting only the distinct ones).

The product of its (nonzero) digits is 10368, while the sum is 30.

The square root of 413293440 is about 20329.6197701777. The cubic root of 413293440 is about 744.8797547775.

The spelling of 413293440 in words is "four hundred thirteen million, two hundred ninety-three thousand, four hundred forty".