34937568461601 has 81 divisors (see below), whose sum is σ = 56477128184217. Its totient is φ = 20802236607360.

The previous prime is 34937568461443. The next prime is 34937568461651. The reversal of 34937568461601 is 10616486573943.

It is a happy number.

The square root of 34937568461601 is 5910801.

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

34937568461601 is a `hidden beast` number, since 3 + 4 + 9 + 3 + 7 + 5 + 6 + 8 + 4 + 616 + 0 + 1 = 666.

It can be written as a sum of positive squares in 4 ways, for example, as 1186999355025 + 33750569106576 = 1089495^2 + 5809524^2 .

It is not a de Polignac number, because 34937568461601 - 2¹⁹ = 34937567937313 is a prime.

It is a super-3 number, since 3×34937568461601³ (a number of 42 digits) contains 333 as substring. Note that it is a super-d number also for d = 2.

It is not an unprimeable number, because it can be changed into a prime (34937568461651) by changing a digit.

It is a polite number, since it can be written in 80 ways as a sum of consecutive naturals, for example, 7146155965 + ... + 7146160853.

Almost surely, 2^{34937568461601} is an apocalyptic number.

34937568461601 is a gapful number since it is divisible by the number (31) formed by its first and last digit.

34937568461601 is the 5910801-st square number.

34937568461601 is the 2955401-st centered octagonal number.

It is an amenable number.

34937568461601 is a deficient number, since it is larger than the sum of its proper divisors (21539559722616).

34937568461601 is an frugal number, since it uses more digits than its factorization.

34937568461601 is an evil number, because the sum of its binary digits is even.

The sum of its prime factors is 9872 (or 4936 counting only the distinct ones).

The product of its (nonzero) digits is 78382080, while the sum is 63.

The spelling of 34937568461601 in words is "thirty-four trillion, nine hundred thirty-seven billion, five hundred sixty-eight million, four hundred sixty-one thousand, six hundred one".