417616128 has 144 divisors (see below), whose sum is σ = 1275456000. Its totient is φ = 134645760.

The previous prime is 417616081. The next prime is 417616183. The reversal of 417616128 is 821616714.

It is a happy number.

417616128 is a `hidden beast` number, since 4 + 17 + 616 + 1 + 28 = 666.

It is a tau number, because it is divible by the number of its divisors (144).

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 = 417616092 and 417616101.

It is an unprimeable number.

It is a polite number, since it can be written in 15 ways as a sum of consecutive naturals, for example, 213298 + ... + 215246.

Almost surely, 2^417616128 is an apocalyptic number.

417616128 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 417616128, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (637728000).

417616128 is an abundant number, since it is smaller than the sum of its proper divisors (857839872).

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

417616128 is a wasteful number, since it uses less digits than its factorization.

417616128 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 2005 (or 1985 counting only the distinct ones).

The product of its digits is 16128, while the sum is 36.

The square root of 417616128 is about 20435.6582472892. The cubic root of 417616128 is about 747.4676834535.

The spelling of 417616128 in words is "four hundred seventeen million, six hundred sixteen thousand, one hundred twenty-eight".