511142400 has 600 divisors, whose sum is σ = 2072127420. Its totient is φ = 123863040.

The previous prime is 511142393. The next prime is 511142453. The reversal of 511142400 is 4241115.

It can be written as a sum of positive squares in 6 ways, for example, as 264777984 + 246364416 = 16272^2 + 15696^2 .

It is a tau number, because it is divible by the number of its divisors (600).

It is a super-2 number, since 2×511142400² = 522533106155520000, which contains 22 as substring.

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, 17625586 + ... + 17625614.

Almost surely, 2^511142400 is an apocalyptic number.

511142400 is a gapful number since it is divisible by the number (50) 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 511142400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (1036063710).

511142400 is an abundant number, since it is smaller than the sum of its proper divisors (1560985020).

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

511142400 is a wasteful number, since it uses less digits than its factorization.

511142400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 86 (or 56 counting only the distinct ones).

The product of its (nonzero) digits is 160, while the sum is 18.

The square root of 511142400 is about 22608.4585940749. The cubic root of 511142400 is about 799.5530837121.

Adding to 511142400 its reverse (4241115), we get a palindrome (515383515).

The spelling of 511142400 in words is "five hundred eleven million, one hundred forty-two thousand, four hundred".