417006080 has 160 divisors (see below), whose sum is σ = 1067275440. Its totient is φ = 155975680.

The previous prime is 417006059. The next prime is 417006103. The reversal of 417006080 is 80600714.

It can be written as a sum of positive squares in 8 ways, for example, as 91853056 + 325153024 = 9584^2 + 18032^2 .

It is a tau number, because it is divible by the number of its divisors (160).

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, 3043772 + ... + 3043908.

Almost surely, 2^417006080 is an apocalyptic number.

417006080 is a gapful number since it is divisible by the number (40) 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 417006080, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (533637720).

417006080 is an abundant number, since it is smaller than the sum of its proper divisors (650269360).

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

417006080 is a wasteful number, since it uses less digits than its factorization.

417006080 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 230 (or 214 counting only the distinct ones).

The product of its (nonzero) digits is 1344, while the sum is 26.

The square root of 417006080 is about 20420.7267255600. The cubic root of 417006080 is about 747.1035425193.

Adding to 417006080 its reverse (80600714), we get a palindrome (497606794).

The spelling of 417006080 in words is "four hundred seventeen million, six thousand, eighty".