7648537828801 has 9 divisors (see below), whose sum is σ = 7659280645603. Its totient is φ = 7637810070280.

The previous prime is 7648537828783. The next prime is 7648537828859. The reversal of 7648537828801 is 1088287358467.

The square root of 7648537828801 is 2765599.

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., 4742808484401 + 2905729344400 = 2177799^2 + 1704620^2 .

It is not a de Polignac number, because 7648537828801 - 2¹⁷ = 7648537697729 is a prime.

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (7648537828301) 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, 2602427190 + ... + 2602430128.

Almost surely, 2^{7648537828801} is an apocalyptic number.

7648537828801 is the 2765599-th square number.

7648537828801 is the 1382800-th centered octagonal number.

It is an amenable number.

7648537828801 is a deficient number, since it is larger than the sum of its proper divisors (10742816802).

7648537828801 is an frugal number, since it uses more digits than its factorization.

7648537828801 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 7760 (or 3880 counting only the distinct ones).

The product of its (nonzero) digits is 144506880, while the sum is 67.

The spelling of 7648537828801 in words is "seven trillion, six hundred forty-eight billion, five hundred thirty-seven million, eight hundred twenty-eight thousand, eight hundred one".