417372032 has 256 divisors, whose sum is σ = 1142138880. Its totient is φ = 146964480.

The previous prime is 417372029. The next prime is 417372073. The reversal of 417372032 is 230273714.

It is a junction number, because it is equal to n+sod(n) for n = 417371986 and 417372004.

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 31 ways as a sum of consecutive naturals, for example, 7874918 + ... + 7874970.

It is an arithmetic number, because the mean of its divisors is an integer number (4461480).

Almost surely, 2^417372032 is an apocalyptic number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 417372032, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (571069440).

417372032 is an abundant number, since it is smaller than the sum of its proper divisors (724766848).

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

417372032 is a wasteful number, since it uses less digits than its factorization.

417372032 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 149 (or 137 counting only the distinct ones).

The product of its (nonzero) digits is 7056, while the sum is 29.

The square root of 417372032 is about 20429.6850685467. The cubic root of 417372032 is about 747.3220238242.

The spelling of 417372032 in words is "four hundred seventeen million, three hundred seventy-two thousand, thirty-two".