420289129728 has 864 divisors, whose sum is σ = 1509310857600. Its totient is φ = 115235094528.

The previous prime is 420289129727. The next prime is 420289129801. The reversal of 420289129728 is 827921982024.

420289129728 is a `hidden beast` number, since 420 + 28 + 9 + 129 + 72 + 8 = 666.

It is a tau number, because it is divible by the number of its divisors (864).

It is a super-3 number, since 3×420289129728³ (a number of 36 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is a Harshad number since it is a multiple of its sum of digits (54).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (420289129727) by changing a digit.

It is a polite number, since it can be written in 95 ways as a sum of consecutive naturals, for example, 261210588 + ... + 261212196.

Almost surely, 2^420289129728 is an apocalyptic number.

420289129728 is a gapful number since it is divisible by the number (48) 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 420289129728, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (754655428800).

420289129728 is an abundant number, since it is smaller than the sum of its proper divisors (1089021727872).

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

420289129728 is a wasteful number, since it uses less digits than its factorization.

420289129728 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 1689 (or 1663 counting only the distinct ones).

The product of its (nonzero) digits is 2322432, while the sum is 54.

The spelling of 420289129728 in words is "four hundred twenty billion, two hundred eighty-nine million, one hundred twenty-nine thousand, seven hundred twenty-eight".