416752128 has 200 divisors, whose sum is σ = 1341312588. Its totient is φ = 128065536.

The previous prime is 416752103. The next prime is 416752169. The reversal of 416752128 is 821257614.

It can be written as a sum of positive squares in 2 ways, for example, as 334450944 + 82301184 = 18288^2 + 9072^2 .

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 = 416752092 and 416752101.

It is an unprimeable number.

It is a polite number, since it can be written in 19 ways as a sum of consecutive naturals, for example, 538750 + ... + 539522.

Almost surely, 2^416752128 is an apocalyptic number.

416752128 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 416752128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (670656294).

416752128 is an abundant number, since it is smaller than the sum of its proper divisors (924560460).

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

416752128 is an equidigital number, since it uses as much as digits as its factorization.

416752128 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 816 (or 791 counting only the distinct ones).

The product of its digits is 26880, while the sum is 36.

The square root of 416752128 is about 20414.5077824571. The cubic root of 416752128 is about 746.9518525120.

The spelling of 416752128 in words is "four hundred sixteen million, seven hundred fifty-two thousand, one hundred twenty-eight".