101142410132400 has 1440 divisors, whose sum is σ = 425561222338560. Its totient is φ = 20036191518720.

The previous prime is 101142410132389. The next prime is 101142410132429. The reversal of 101142410132400 is 4231014241101.

It is a happy number.

It is a super-2 number, since 2×101142410132400² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (24).

It is an unprimeable number.

It is a pernicious number, because its binary representation contains a prime number (29) of ones.

It is a polite number, since it can be written in 287 ways as a sum of consecutive naturals, for example, 10449670761 + ... + 10449680439.

It is an arithmetic number, because the mean of its divisors is an integer number (295528626624).

Almost surely, 2^{101142410132400} is an apocalyptic number.

101142410132400 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 101142410132400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (212780611169280).

101142410132400 is an abundant number, since it is smaller than the sum of its proper divisors (324418812206160).

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

101142410132400 is a wasteful number, since it uses less digits than its factorization.

101142410132400 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 10183 (or 10159 counting only the distinct ones).

The product of its (nonzero) digits is 768, while the sum is 24.

Adding to 101142410132400 its reverse (4231014241101), we get a palindrome (105373424373501).

The spelling of 101142410132400 in words is "one hundred one trillion, one hundred forty-two billion, four hundred ten million, one hundred thirty-two thousand, four hundred".