1300406400 has 480 divisors, whose sum is σ = 4992956100. Its totient is φ = 332881920.

The previous prime is 1300406377. The next prime is 1300406423. The reversal of 1300406400 is 46040031.

It is an interprime number because it is at equal distance from previous prime (1300406377) and next prime (1300406423).

It can be written as a sum of positive squares in 6 ways, for example, as 792535104 + 507871296 = 28152^2 + 22536^2 .

It is a tau number, because it is divible by the number of its divisors (480).

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 59 ways as a sum of consecutive naturals, for example, 7516714 + ... + 7516886.

Almost surely, 2^1300406400 is an apocalyptic number.

1300406400 is a gapful number since it is divisible by the number (10) 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 1300406400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (2496478050).

1300406400 is an abundant number, since it is smaller than the sum of its proper divisors (3692549700).

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

1300406400 is a wasteful number, since it uses less digits than its factorization.

1300406400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 238 (or 212 counting only the distinct ones).

The product of its (nonzero) digits is 288, while the sum is 18.

The square root of 1300406400 is about 36061.1480682465. The cubic root of 1300406400 is about 1091.5065999473.

Adding to 1300406400 its reverse (46040031), we get a palindrome (1346446431).

The spelling of 1300406400 in words is "one billion, three hundred million, four hundred six thousand, four hundred".