417327628081 has 81 divisors (see below), whose sum is σ = 545565322593. Its totient is φ = 318146512320.

The previous prime is 417327628049. The next prime is 417327628087. The reversal of 417327628081 is 180826723714.

The square root of 417327628081 is 646009.

It is a perfect power (a square), and thus also a powerful number.

It can be written as a sum of positive squares in 4 ways, for example, as 6979767025 + 410347861056 = 83545^2 + 640584^2 .

It is not a de Polignac number, because 417327628081 - 2⁵ = 417327628049 is a prime.

It is a super-2 number, since 2×417327628081² (a number of 24 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (49).

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (417327628087) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 1822391275 + ... + 1822391503.

It is an arithmetic number, because the mean of its divisors is an integer number (6735374353).

Almost surely, 2^417327628081 is an apocalyptic number.

417327628081 is the 646009-th square number.

417327628081 is the 323005-th centered octagonal number.

It is an amenable number.

417327628081 is a deficient number, since it is larger than the sum of its proper divisors (128237694512).

417327628081 is an equidigital number, since it uses as much as digits as its factorization.

417327628081 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 560 (or 280 counting only the distinct ones).

The product of its (nonzero) digits is 903168, while the sum is 49.

Multiplying 417327628081 by its sum of digits (49), we get a square (20449053775969 = 4522063²).

417327628081 divided by its sum of digits (49) gives a square (8516890369 = 92287²).

The spelling of 417327628081 in words is "four hundred seventeen billion, three hundred twenty-seven million, six hundred twenty-eight thousand, eighty-one".