413514000 has 120 divisors (see below), whose sum is σ = 1444329432. Its totient is φ = 110265600.

The previous prime is 413513983. The next prime is 413514041. The reversal of 413514000 is 415314.

It is a happy number.

It can be written as a sum of positive squares in 4 ways, for example, as 12873744 + 400640256 = 3588^2 + 20016^2 .

It is a tau number, because it is divible by the number of its divisors (120).

It is a Harshad number since it is a multiple of its sum of digits (18).

It is an unprimeable number.

It is a polite number, since it can be written in 23 ways as a sum of consecutive naturals, for example, 6514 + ... + 29486.

Almost surely, 2^413514000 is an apocalyptic number.

413514000 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 413514000, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (722164716).

413514000 is an abundant number, since it is smaller than the sum of its proper divisors (1030815432).

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

413514000 is a wasteful number, since it uses less digits than its factorization.

413514000 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 23002 (or 22983 counting only the distinct ones).

The product of its (nonzero) digits is 240, while the sum is 18.

The square root of 413514000 is about 20335.0436439168. The cubic root of 413514000 is about 745.0122364851.

Adding to 413514000 its reverse (415314), we get a palindrome (413929314).

The spelling of 413514000 in words is "four hundred thirteen million, five hundred fourteen thousand".