Number of the day: 34801

Nikolai Lobachevsky was born on this day 226 years ago.

Properties of the number 34801:

34801 is a cyclic number.
34801 = 13 × 2677 is semiprime and squarefree.
34801 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 32112 totatives.
Reversing the decimal digits of 34801 results in an emirpimes.
34801 = 17401² - 17400² = 1345² - 1332² is the difference of 2 nonnegative squares in 2 ways.
34801 is the difference of 2 positive pentagonal numbers in 2 ways.
34801 = 49² + 180² = 24² + 185² is the sum of 2 positive squares in 2 ways.
34801 = 4² + 81² + 168² is the sum of 3 positive squares.
34801² = 13385² + 32124² = 8880² + 33649² = 17640² + 29999² = 4745² + 34476² is the sum of 2 positive squares in 4 ways.
34801² is the sum of 3 positive squares.
34801 is a proper divisor of 1033¹² - 1.
34801 = '3' + '4801' is the concatenation of 2 prime numbers.
34801 is an emirpimes in (at least) the following bases: 3, 9, 10, 17, 22, 25, 26, 27, 28, 29, 31, 33, 35, 37, 41, 42, 44, 45, 48, 49, 51, 53, 55, 57, 58, 60, 62, 63, 65, 68, 69, 71, 73, 76, 77, 78, 81, 85, 89, 95, 96, 97, and 100.
34801 is palindromic in (at least) the following bases: 12, -15, and -52.
34801 in base 12 = 18181 and consists of only the digits '1' and '8'.
34801 in base 33 = vvj and consists of only the digits 'j' and 'v'.
34801 in base 51 = DJJ and consists of only the digits 'D' and 'J'.

The number 34801 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A020418: Numbers n such that continued fraction for sqrt(n) has period 79.
A135712: a(n) = (4*n^3 + 11*n^2 + 9*n + 2)/2.
A291543: Array read by antidiagonals: T(m,n) = number of maximal irredundant sets in the lattice (rook) graph K_m X K_n.
A303196: Number of nX7 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
A303201: Number of 6Xn 0..1 arrays with every element equal to 0, 1, 3, 5 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.