1001417284800 has 504 divisors, whose sum is σ = 3668803119072. Its totient is φ = 258951168000.

The previous prime is 1001417284793. The next prime is 1001417284823. The reversal of 1001417284800 is 84827141001.

1001417284800 is a `hidden beast` number, since 1 + 0 + 0 + 1 + 4 + 172 + 8 + 480 + 0 = 666.

It is a super-2 number, since 2×1001417284800² (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 71 ways as a sum of consecutive naturals, for example, 62358372 + ... + 62374428.

It is an arithmetic number, because the mean of its divisors is an integer number (7279371268).

Almost surely, 2^{1001417284800} is an apocalyptic number.

1001417284800 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 1001417284800, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1834401559536).

1001417284800 is an abundant number, since it is smaller than the sum of its proper divisors (2667385834272).

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

1001417284800 is a wasteful number, since it uses less digits than its factorization.

1001417284800 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 16217 (or 16199 counting only the distinct ones).

The product of its (nonzero) digits is 14336, while the sum is 36.

The spelling of 1001417284800 in words is "one trillion, one billion, four hundred seventeen million, two hundred eighty-four thousand, eight hundred".