138095378457201 has 189 divisors, whose sum is σ = 229955292048027. Its totient is φ = 82926332351280.

The previous prime is 138095378457077. The next prime is 138095378457229. The reversal of 138095378457201 is 102754873590831.

It is a happy number.

The square root of 138095378457201 is 11751399.

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

138095378457201 is a `hidden beast` number, since 1 + 3 + 8 + 0 + 9 + 5 + 378 + 4 + 57 + 201 = 666.

It can be written as a sum of positive squares in only one way, i.e., 96251816261601 + 41843562195600 = 9810801^2 + 6468660^2 .

It is not a de Polignac number, because 138095378457201 - 2²⁵ = 138095344902769 is a prime.

It is not an unprimeable number, because it can be changed into a prime (138095378457601) by changing a digit.

It is a polite number, since it can be written in 188 ways as a sum of consecutive naturals, for example, 1266930077535 + ... + 1266930077643.

Almost surely, 2^{138095378457201} is an apocalyptic number.

138095378457201 is a gapful number since it is divisible by the number (11) formed by its first and last digit.

138095378457201 is the 11751399-th square number.

138095378457201 is the 5875700-th centered octagonal number.

It is an amenable number.

138095378457201 is a deficient number, since it is larger than the sum of its proper divisors (91859913590826).

138095378457201 is an frugal number, since it uses more digits than its factorization.

138095378457201 is an odious number, because the sum of its binary digits is odd.

The sum of its prime factors is 308 (or 123 counting only the distinct ones).

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

The spelling of 138095378457201 in words is "one hundred thirty-eight trillion, ninety-five billion, three hundred seventy-eight million, four hundred fifty-seven thousand, two hundred one".