1288724448400 has 135 divisors (see below), whose sum is σ = 3201006671289. Its totient is φ = 498588624000.

The previous prime is 1288724448383. The next prime is 1288724448419. The reversal of 1288724448400 is 48444278821.

The square root of 1288724448400 is 1135220.

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., 463940801424 + 824783646976 = 681132^2 + 908176^2 .

It is a Smith number, since the sum of its digits (52) coincides with the sum of the digits of its prime factors.

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 703835485 + ... + 703837315.

Almost surely, 2^{1288724448400} is an apocalyptic number.

1288724448400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1288724448400 is the 1135220-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1288724448400

1288724448400 is an abundant number, since it is smaller than the sum of its proper divisors (1912282222889).

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

1288724448400 is an frugal number, since it uses more digits than its factorization.

1288724448400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 3742 (or 1869 counting only the distinct ones).

The product of its (nonzero) digits is 3670016, while the sum is 52.

It can be divided in two parts, 1288724 and 448400, that added together give a square (1737124 = 1318²).

The spelling of 1288724448400 in words is "one trillion, two hundred eighty-eight billion, seven hundred twenty-four million, four hundred forty-eight thousand, four hundred".