420478400160 has 2160 divisors, whose sum is σ = 1957145302728. Its totient is φ = 84234608640.

The previous prime is 420478400141. The next prime is 420478400171. The reversal of 420478400160 is 61004874024.

420478400160 is a `hidden beast` number, since 4 + 20 + 4 + 78 + 400 + 160 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 307638841104 + 112839559056 = 554652^2 + 335916^2 .

It is a tau number, because it is divible by the number of its divisors (2160).

It is a super-2 number, since 2×420478400160² (a number of 24 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 359 ways as a sum of consecutive naturals, for example, 7933554694 + ... + 7933554746.

Almost surely, 2^420478400160 is an apocalyptic number.

420478400160 is a gapful number since it is divisible by the number (40) 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 420478400160, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (978572651364).

420478400160 is an abundant number, since it is smaller than the sum of its proper divisors (1536666902568).

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

420478400160 is a wasteful number, since it uses less digits than its factorization.

420478400160 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 169 (or 114 counting only the distinct ones).

The product of its (nonzero) digits is 43008, while the sum is 36.

The spelling of 420478400160 in words is "four hundred twenty billion, four hundred seventy-eight million, four hundred thousand, one hundred sixty".