413408071440 has 960 divisors, whose sum is σ = 1811876032512. Its totient is φ = 82114560000.

The previous prime is 413408071429. The next prime is 413408071459. The reversal of 413408071440 is 44170804314.

It is a happy number.

413408071440 is a `hidden beast` number, since 4 + 134 + 0 + 80 + 7 + 1 + 440 = 666.

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

It is a junction number, because it is equal to n+sod(n) for n = 413408071395 and 413408071404.

It is an unprimeable number.

It is a polite number, since it can be written in 191 ways as a sum of consecutive naturals, for example, 75148690 + ... + 75154190.

Almost surely, 2^413408071440 is an apocalyptic number.

413408071440 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 413408071440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (905938016256).

413408071440 is an abundant number, since it is smaller than the sum of its proper divisors (1398467961072).

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

413408071440 is a wasteful number, since it uses less digits than its factorization.

413408071440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 5608 (or 5599 counting only the distinct ones).

The product of its (nonzero) digits is 43008, while the sum is 36.

Adding to 413408071440 its reverse (44170804314), we get a palindrome (457578875754).

The spelling of 413408071440 in words is "four hundred thirteen billion, four hundred eight million, seventy-one thousand, four hundred forty".