407185648321 has 9 divisors (see below), whose sum is σ = 410893712931. Its totient is φ = 403510767072.

The previous prime is 407185648279. The next prime is 407185648339. The reversal of 407185648321 is 123846581704.

The square root of 407185648321 is 638111.

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

It can be written as a sum of positive squares in only one way, i.e., 7174937025 + 400010711296 = 84705^2 + 632464^2 .

It is not a de Polignac number, because 407185648321 - 2¹³ = 407185640129 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (407185648391) by changing a digit.

It is a polite number, since it can be written in 8 ways as a sum of consecutive naturals, for example, 72103720 + ... + 72109366.

Almost surely, 2^407185648321 is an apocalyptic number.

407185648321 is the 638111-st square number.

407185648321 is the 319056-th centered octagonal number.

It is an amenable number.

407185648321 is a deficient number, since it is larger than the sum of its proper divisors (3708064610).

407185648321 is an frugal number, since it uses more digits than its factorization.

407185648321 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 11520 (or 5760 counting only the distinct ones).

The product of its (nonzero) digits is 1290240, while the sum is 49.

Multiplying 407185648321 by its sum of digits (49), we get a square (19952096767729 = 4466777²).

The spelling of 407185648321 in words is "four hundred seven billion, one hundred eighty-five million, six hundred forty-eight thousand, three hundred twenty-one".