101006125660440 has 1536 divisors, whose sum is σ = 468277247692800. Its totient is φ = 18200109957120.

The previous prime is 101006125660417. The next prime is 101006125660501. The reversal of 101006125660440 is 44066521600101.

101006125660440 is a `hidden beast` number, since 1 + 0 + 1 + 0 + 0 + 6 + 1 + 2 + 5 + 6 + 604 + 40 = 666.

It is a Harshad number since it is a multiple of its sum of digits (36).

It is a junction number, because it is equal to n+sod(n) for n = 101006125660395 and 101006125660404.

It is a congruent number.

It is an unprimeable number.

It is a polite number, since it can be written in 383 ways as a sum of consecutive naturals, for example, 386535669 + ... + 386796891.

It is an arithmetic number, because the mean of its divisors is an integer number (304867999800).

Almost surely, 2^{101006125660440} is an apocalyptic number.

101006125660440 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 101006125660440, and also a Zumkeller number, because its divisors can be partitioned in two sets with the same sum (234138623846400).

101006125660440 is an abundant number, since it is smaller than the sum of its proper divisors (367271122032360).

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

101006125660440 is a wasteful number, since it uses less digits than its factorization.

101006125660440 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 261337 (or 261330 counting only the distinct ones).

The product of its (nonzero) digits is 34560, while the sum is 36.

The spelling of 101006125660440 in words is "one hundred one trillion, six billion, one hundred twenty-five million, six hundred sixty thousand, four hundred forty".