101610400 has 72 divisors (see below), whose sum is σ = 249944940. Its totient is φ = 40335360.

The previous prime is 101610373. The next prime is 101610407. The reversal of 101610400 is 4016101.

It can be written as a sum of positive squares in 6 ways, for example, as 47499664 + 54110736 = 6892^2 + 7356^2 .

It is not an unprimeable number, because it can be changed into a prime (101610407) by changing a digit.

It is a polite number, since it can be written in 11 ways as a sum of consecutive naturals, for example, 125196 + ... + 126004.

Almost surely, 2^101610400 is an apocalyptic number.

101610400 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 101610400, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (124972470).

101610400 is an abundant number, since it is smaller than the sum of its proper divisors (148334540).

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

101610400 is a wasteful number, since it uses less digits than its factorization.

101610400 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 986 (or 973 counting only the distinct ones).

The product of its (nonzero) digits is 24, while the sum is 13.

The square root of 101610400 is about 10080.1984107457. The cubic root of 101610400 is about 466.6372317035.

Adding to 101610400 its reverse (4016101), we get a palindrome (105626501).

The spelling of 101610400 in words is "one hundred one million, six hundred ten thousand, four hundred".