413124608457792 has 2688 divisors, whose sum is σ = 1592980049756160. Its totient is φ = 99273517056000.

The previous prime is 413124608457727. The next prime is 413124608457817. The reversal of 413124608457792 is 297754806421314.

413124608457792 is a `hidden beast` number, since 4 + 1 + 3 + 1 + 2 + 460 + 84 + 5 + 7 + 7 + 92 = 666.

It is a super-2 number, since 2×413124608457792² (a number of 30 digits) contains 22 as substring.

It is a hoax number, since the sum of its digits (63) coincides with the sum of the digits of its distinct prime factors.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 582686330334 + ... + 582686331042.

It is a 1-persistent number, because it is pandigital, but 2⋅413124608457792 = 826249216915584 is not.

Almost surely, 2^{413124608457792} is an apocalyptic number.

413124608457792 is a gapful number since it is divisible by the number (42) 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 413124608457792, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (796490024878080).

413124608457792 is an abundant number, since it is smaller than the sum of its proper divisors (1179855441298368).

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

413124608457792 is a wasteful number, since it uses less digits than its factorization.

413124608457792 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1021 (or 1008 counting only the distinct ones).

The product of its (nonzero) digits is 81285120, while the sum is 63.

The spelling of 413124608457792 in words is "four hundred thirteen trillion, one hundred twenty-four billion, six hundred eight million, four hundred fifty-seven thousand, seven hundred ninety-two".