407310727681 has 27 divisors (see below), whose sum is σ = 484901832387. Its totient is φ = 341722626960.

The previous prime is 407310727669. The next prime is 407310727693. The reversal of 407310727681 is 186727013704.

The square root of 407310727681 is 638209.

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

It is an interprime number because it is at equal distance from previous prime (407310727669) and next prime (407310727693).

It can be written as a sum of positive squares in only one way, i.e., 60253066225 + 347057661456 = 245465^2 + 589116^2 .

It is not a de Polignac number, because 407310727681 - 2⁷ = 407310727553 is a prime.

It is a super-4 number, since 4×407310727681⁴ (a number of 48 digits) contains 4444 as substring. Note that it is a super-d number also for d = 2.

It is a Smith number, since the sum of its digits (46) coincides with the sum of the digits of its prime factors.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (407310727601) by changing a digit.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 91261656 + ... + 91266118.

Almost surely, 2^407310727681 is an apocalyptic number.

407310727681 is the 638209-th square number.

407310727681 is the 319105-th centered octagonal number.

It is an amenable number.

407310727681 is a deficient number, since it is larger than the sum of its proper divisors (77591104706).

407310727681 is an frugal number, since it uses more digits than its factorization.

407310727681 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 8974 (or 4487 counting only the distinct ones).

The product of its (nonzero) digits is 395136, while the sum is 46.

The spelling of 407310727681 in words is "four hundred seven billion, three hundred ten million, seven hundred twenty-seven thousand, six hundred eighty-one".