1585030640400 has 135 divisors (see below), whose sum is σ = 5500758761589. Its totient is φ = 422654693760.

The previous prime is 1585030640393. The next prime is 1585030640443. The reversal of 1585030640400 is 40460305851.

It is a happy number.

The square root of 1585030640400 is 1258980.

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

1585030640400 is a `hidden beast` number, since 1 + 5 + 8 + 5 + 0 + 3 + 0 + 640 + 4 + 0 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 570611030544 + 1014419609856 = 755388^2 + 1007184^2 .

It is a super-2 number, since 2×1585030640400² (a number of 25 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is an unprimeable number.

It is a polite number, since it can be written in 26 ways as a sum of consecutive naturals, for example, 75528309 + ... + 75549291.

Almost surely, 2^{1585030640400} is an apocalyptic number.

1585030640400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

1585030640400 is the 1258980-th square number.

It is an amenable number.

1585030640400 is an abundant number, since it is smaller than the sum of its proper divisors (3915728121189).

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

1585030640400 is an frugal number, since it uses more digits than its factorization.

1585030640400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 41990 (or 20993 counting only the distinct ones).

The product of its (nonzero) digits is 57600, while the sum is 36.

Multiplying 1585030640400 by its sum of digits (36), we get a square (57061103054400 = 7553880²).

1585030640400 divided by its sum of digits (36) gives a square (44028628900 = 209830²).

The spelling of 1585030640400 in words is "one trillion, five hundred eighty-five billion, thirty million, six hundred forty thousand, four hundred".