84105975406761 has 405 divisors, whose sum is σ = 165346161503523. Its totient is φ = 41044685109120.

The previous prime is 84105975406721. The next prime is 84105975406763. The reversal of 84105975406761 is 16760457950148.

The square root of 84105975406761 is 9170931.

It is a perfect power (a square), and thus also a powerful number.

84105975406761 is a `hidden beast` number, since 8 + 4 + 10 + 5 + 9 + 7 + 540 + 6 + 76 + 1 = 666.

It can be written as a sum of positive squares in 7 ways, for example, as 1858126123161 + 82247849283600 = 1363131^2 + 9069060^2 .

It is not a de Polignac number, because 84105975406761 - 2¹⁷ = 84105975275689 is a prime.

It is a super-2 number, since 2×84105975406761² (a number of 29 digits) contains 22 as substring.

It is a Harshad number since it is a multiple of its sum of digits (63).

It is not an unprimeable number, because it can be changed into a prime (84105975406763) by changing a digit.

It is a pernicious number, because its binary representation contains a prime number (23) of ones.

It is a polite number, since it can be written in 404 ways as a sum of consecutive naturals, for example, 2273134470435 + ... + 2273134470471.

Almost surely, 2^{84105975406761} is an apocalyptic number.

84105975406761 is the 9170931-st square number.

84105975406761 is the 4585466-th centered octagonal number.

It is an amenable number.

84105975406761 is a deficient number, since it is larger than the sum of its proper divisors (81240186096762).

84105975406761 is an frugal number, since it uses more digits than its factorization.

84105975406761 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 248 (or 87 counting only the distinct ones).

The product of its (nonzero) digits is 50803200, while the sum is 63.

The spelling of 84105975406761 in words is "eighty-four trillion, one hundred five billion, nine hundred seventy-five million, four hundred six thousand, seven hundred sixty-one".