413023968 has 192 divisors, whose sum is σ = 1407006720. Its totient is φ = 115416576.

The previous prime is 413023951. The next prime is 413023973. The reversal of 413023968 is 869320314.

413023968 is a `hidden beast` number, since 413 + 0 + 239 + 6 + 8 = 666.

It is a hoax number, since the sum of its digits (36) 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 (36).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 31 ways as a sum of consecutive naturals, for example, 283530 + ... + 284982.

It is an arithmetic number, because the mean of its divisors is an integer number (7328160).

Almost surely, 2^413023968 is an apocalyptic number.

413023968 is a gapful number since it is divisible by the number (48) 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 413023968, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (703503360).

413023968 is an abundant number, since it is smaller than the sum of its proper divisors (993982752).

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

413023968 is a wasteful number, since it uses less digits than its factorization.

413023968 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1526 (or 1512 counting only the distinct ones).

The product of its (nonzero) digits is 31104, while the sum is 36.

The square root of 413023968 is about 20322.9911184353. The cubic root of 413023968 is about 744.7178295701.

The spelling of 413023968 in words is "four hundred thirteen million, twenty-three thousand, nine hundred sixty-eight".