1006576778089 has 27 divisors (see below), whose sum is σ = 1062498027717. Its totient is φ = 953520163200.

The previous prime is 1006576778029. The next prime is 1006576778101. The reversal of 1006576778089 is 9808776756001.

The square root of 1006576778089 is 1003283.

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 164403488089 + 842173290000 = 405467^2 + 917700^2 .

It is not a de Polignac number, because 1006576778089 - 2¹¹ = 1006576776041 is a prime.

It is a Duffinian number.

It is a self number, because there is not a number n which added to its sum of digits gives 1006576778089.

It is not an unprimeable number, because it can be changed into a prime (1006576778029) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 4176667009 + ... + 4176667249.

Almost surely, 2^{1006576778089} is an apocalyptic number.

1006576778089 is the 1003283-rd square number.

1006576778089 is the 501642-nd centered octagonal number.

It is an amenable number.

1006576778089 is a deficient number, since it is larger than the sum of its proper divisors (55921249628).

1006576778089 is an frugal number, since it uses more digits than its factorization.

1006576778089 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 890 (or 445 counting only the distinct ones).

The product of its (nonzero) digits is 35562240, while the sum is 64.

Multiplying 1006576778089 by its sum of digits (64), we get a square (64420913797696 = 8026264²).

The spelling of 1006576778089 in words is "one trillion, six billion, five hundred seventy-six million, seven hundred seventy-eight thousand, eighty-nine".