414001042400 has 144 divisors (see below), whose sum is σ = 1129452741648. Its totient is φ = 146873856000.

The previous prime is 414001042397. The next prime is 414001042421. The reversal of 414001042400 is 4240100414.

It is a happy number.

It is a Harshad number since it is a multiple of its sum of digits (20).

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 212927 + ... + 934526.

It is an arithmetic number, because the mean of its divisors is an integer number (7843421817).

Almost surely, 2^414001042400 is an apocalyptic number.

414001042400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

It is an amenable number.

414001042400 is an abundant number, since it is smaller than the sum of its proper divisors (715451699248).

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

414001042400 is a wasteful number, since it uses less digits than its factorization.

414001042400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 1147525 (or 1147512 counting only the distinct ones).

The product of its (nonzero) digits is 512, while the sum is 20.

Adding to 414001042400 its reverse (4240100414), we get a palindrome (418241142814).

The spelling of 414001042400 in words is "four hundred fourteen billion, one million, forty-two thousand, four hundred".