420059534400 has 567 divisors, whose sum is σ = 1644405045829. Its totient is φ = 101625216000.

The previous prime is 420059534353. The next prime is 420059534413. The reversal of 420059534400 is 4435950024.

It is a happy number.

The square root of 420059534400 is 648120.

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

420059534400 is a `hidden beast` number, since 4 + 20 + 0 + 595 + 3 + 4 + 40 + 0 = 666.

It can be written as a sum of positive squares in only one way, i.e., 151221432384 + 268838102016 = 388872^2 + 518496^2 .

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

It is a Duffinian number.

It is an unprimeable number.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 855518155 + ... + 855518645.

Almost surely, 2^420059534400 is an apocalyptic number.

420059534400 is a gapful number since it is divisible by the number (40) formed by its first and last digit.

420059534400 is the 648120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 420059534400

420059534400 is an abundant number, since it is smaller than the sum of its proper divisors (1224345511429).

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

420059534400 is a wasteful number, since it uses less digits than its factorization.

420059534400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1032 (or 512 counting only the distinct ones).

The product of its (nonzero) digits is 86400, while the sum is 36.

Multiplying 420059534400 by its sum of digits (36), we get a square (15122143238400 = 3888720²).

420059534400 divided by its sum of digits (36) gives a square (11668320400 = 108020²).

It can be divided in two parts, 420059 and 534400, that added together give a palindrome (954459).

The spelling of 420059534400 in words is "four hundred twenty billion, fifty-nine million, five hundred thirty-four thousand, four hundred".