409289760000 has 1890 divisors, whose sum is σ = 1740463787370. Its totient is φ = 95800320000.

The previous prime is 409289759981. The next prime is 409289760001. The reversal of 409289760000 is 67982904.

It is a happy number.

It can be written as a sum of positive squares in 5 ways, for example, as 155563981056 + 253725778944 = 394416^2 + 503712^2 .

It is a Harshad number since it is a multiple of its sum of digits (45).

It is a congruent number.

It is not an unprimeable number, because it can be changed into a prime (409289760001) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (17) of ones.

It is a polite number, since it can be written in 209 ways as a sum of consecutive naturals, for example, 14113439986 + ... + 14113440014.

Almost surely, 2^409289760000 is an apocalyptic number.

409289760000 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 409289760000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (870231893685).

409289760000 is an abundant number, since it is smaller than the sum of its proper divisors (1331174027370).

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

409289760000 is an frugal number, since it uses more digits than its factorization.

409289760000 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 105 (or 50 counting only the distinct ones).

The product of its (nonzero) digits is 217728, while the sum is 45.

The spelling of 409289760000 in words is "four hundred nine billion, two hundred eighty-nine million, seven hundred sixty thousand".