1292417078400 has 1152 divisors, whose sum is σ = 5491498521600. Its totient is φ = 294014914560.

The previous prime is 1292417078389. The next prime is 1292417078429. The reversal of 1292417078400 is 48707142921.

1292417078400 is a `hidden beast` number, since 1 + 2 + 9 + 2 + 4 + 170 + 78 + 400 = 666.

It is a tau number, because it is divible by the number of its divisors (1152).

It is a Harshad number since it is a multiple of its sum of digits (45).

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 143 ways as a sum of consecutive naturals, for example, 1540425181 + ... + 1540426019.

It is an arithmetic number, because the mean of its divisors is an integer number (4766925800).

Almost surely, 2^{1292417078400} is an apocalyptic number.

1292417078400 is a gapful number since it is divisible by the number (10) formed by its first and last digit.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 1292417078400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2745749260800).

1292417078400 is an abundant number, since it is smaller than the sum of its proper divisors (4199081443200).

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

1292417078400 is an equidigital number, since it uses as much as digits as its factorization.

1292417078400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1168 (or 1139 counting only the distinct ones).

The product of its (nonzero) digits is 225792, while the sum is 45.

The spelling of 1292417078400 in words is "one trillion, two hundred ninety-two billion, four hundred seventeen million, seventy-eight thousand, four hundred".