409963100040 has 320 divisors, whose sum is σ = 1492732810800. Its totient is φ = 100912241664.

The previous prime is 409963100023. The next prime is 409963100047. The reversal of 409963100040 is 40001369904.

It can be written as a sum of positive squares in 8 ways, for example, as 72502024644 + 337461075396 = 269262^2 + 580914^2 .

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

It is a junction number, because it is equal to n+sod(n) for n = 409963099968 and 409963100004.

It is not an unprimeable number, because it can be changed into a prime (409963100047) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 79 ways as a sum of consecutive naturals, for example, 7089484 + ... + 7147076.

Almost surely, 2^409963100040 is an apocalyptic number.

409963100040 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 409963100040, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (746366405400).

409963100040 is an abundant number, since it is smaller than the sum of its proper divisors (1082769710760).

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

409963100040 is a wasteful number, since it uses less digits than its factorization.

409963100040 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 57655 (or 57616 counting only the distinct ones).

The product of its (nonzero) digits is 23328, while the sum is 36.

Adding to 409963100040 its reverse (40001369904), we get a palindrome (449964469944).

The spelling of 409963100040 in words is "four hundred nine billion, nine hundred sixty-three million, one hundred thousand, forty".