135862312688001 has 405 divisors, whose sum is σ = 232761844982667. Its totient is φ = 78954939786240.

The previous prime is 135862312687991. The next prime is 135862312688027. The reversal of 135862312688001 is 100886213268531.

The square root of 135862312688001 is 11655999.

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

135862312688001 is a `hidden beast` number, since 1 + 3 + 5 + 8 + 623 + 1 + 2 + 6 + 8 + 8 + 0 + 0 + 1 = 666.

It can be written as a sum of positive squares in 13 ways, for example, as 14895958401 + 135847416729600 = 122049^2 + 11655360^2 .

It is not a de Polignac number, because 135862312688001 - 2²¹ = 135862310590849 is a prime.

It is not an unprimeable number, because it can be changed into a prime (135862312688801) 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, 1913553699796 + ... + 1913553699866.

Almost surely, 2^{135862312688001} is an apocalyptic number.

135862312688001 is the 11655999-th square number.

135862312688001 is the 5828000-th centered octagonal number.

It is an amenable number.

135862312688001 is a deficient number, since it is larger than the sum of its proper divisors (96899532294666).

135862312688001 is an frugal number, since it uses more digits than its factorization.

135862312688001 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 320 (or 157 counting only the distinct ones).

The product of its (nonzero) digits is 3317760, while the sum is 54.

The spelling of 135862312688001 in words is "one hundred thirty-five trillion, eight hundred sixty-two billion, three hundred twelve million, six hundred eighty-eight thousand, one".