1251413456400 has 180 divisors, whose sum is σ = 4343218684740. Its totient is φ = 333674419200.

The previous prime is 1251413456393. The next prime is 1251413456407. The reversal of 1251413456400 is 46543141521.

1251413456400 is a `hidden beast` number, since 1 + 2 + 5 + 1 + 4 + 1 + 3 + 4 + 5 + 640 + 0 = 666.

It is an interprime number because it is at equal distance from previous prime (1251413456393) and next prime (1251413456407).

It can be written as a sum of positive squares in 6 ways, for example, as 2419459344 + 1248993997056 = 49188^2 + 1117584^2 .

It is a tau number, because it is divible by the number of its divisors (180).

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

It is not an unprimeable number, because it can be changed into a prime (1251413456407) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (19) of ones.

It is a polite number, since it can be written in 35 ways as a sum of consecutive naturals, for example, 64030630 + ... + 64050170.

It is an arithmetic number, because the mean of its divisors is an integer number (24128992693).

Almost surely, 2^{1251413456400} is an apocalyptic number.

1251413456400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

1251413456400 is an abundant number, since it is smaller than the sum of its proper divisors (3091805228340).

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

1251413456400 is a wasteful number, since it uses less digits than its factorization.

1251413456400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 37354 (or 37340 counting only the distinct ones).

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

Adding to 1251413456400 its reverse (46543141521), we get a palindrome (1297956597921).

The spelling of 1251413456400 in words is "one trillion, two hundred fifty-one billion, four hundred thirteen million, four hundred fifty-six thousand, four hundred".