81293414400 has 1053 divisors, whose sum is σ = 332345262613. Its totient is φ = 19707494400.

The previous prime is 81293414327. The next prime is 81293414407. The reversal of 81293414400 is 441439218.

It is a happy number.

The square root of 81293414400 is 285120.

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

It can be written as a sum of positive squares in only one way, i.e., 29265629184 + 52027785216 = 171072^2 + 228096^2 .

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

It is a Duffinian number.

It is not an unprimeable number, because it can be changed into a prime (81293414407) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 7390310395 + ... + 7390310405.

Almost surely, 2^81293414400 is an apocalyptic number.

81293414400 is a gapful number since it is divisible by the number (80) formed by its first and last digit.

81293414400 is the 285120-th square number.

It is an amenable number.

It is a practical number, because each smaller number is the sum of distinct divisors of 81293414400

81293414400 is an abundant number, since it is smaller than the sum of its proper divisors (251051848213).

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

81293414400 is an frugal number, since it uses more digits than its factorization.

81293414400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 80 (or 21 counting only the distinct ones).

The product of its (nonzero) digits is 27648, while the sum is 36.

Multiplying 81293414400 by its sum of digits (36), we get a square (2926562918400 = 1710720²).

81293414400 divided by its sum of digits (36) gives a square (2258150400 = 47520²).

The spelling of 81293414400 in words is "eighty-one billion, two hundred ninety-three million, four hundred fourteen thousand, four hundred".