401013000 has 192 divisors, whose sum is σ = 1435702320. Its totient is φ = 100608000.

The previous prime is 401012987. The next prime is 401013001. The reversal of 401013000 is 310104.

It can be written as a sum of positive squares in 8 ways, for example, as 93431556 + 307581444 = 9666^2 + 17538^2 .

It is a super-2 number, since 2×401013000² = 321622852338000000, which contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (9).

It is not an unprimeable number, because it can be changed into a prime (401013001) by changing a digit.

It is a polite number, since it can be written in 47 ways as a sum of consecutive naturals, for example, 151690 + ... + 154310.

Almost surely, 2^401013000 is an apocalyptic number.

401013000 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 401013000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (717851160).

401013000 is an abundant number, since it is smaller than the sum of its proper divisors (1034689320).

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

401013000 is a wasteful number, since it uses less digits than its factorization.

401013000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 2665 (or 2648 counting only the distinct ones).

The product of its (nonzero) digits is 12, while the sum is 9.

The square root of 401013000 is about 20025.3089863802. The cubic root of 401013000 is about 737.4277627226.

Adding to 401013000 its reverse (310104), we get a palindrome (401323104).

The spelling of 401013000 in words is "four hundred one million, thirteen thousand".