Number of the day: 6801

Stefan Banach was born on this day 127 years ago.

Properties of the number 6801:

6801 is a cyclic number.
6801 = 3 × 2267 is semiprime and squarefree.
6801 has 2 distinct prime factors, 4 divisors, 11 antidivisors and 4532 totatives.
6801 has an emirpimes digit sum 15 in base 10.
6801 has a triangular digit sum 15 in base 10.
Reversing the decimal digits of 6801 results in a sphenic number.
6801 = (18 × 19)/2 + … + (35 × 36)/2 is the sum of at least 2 consecutive triangular numbers in 1 way.
6801 = 3401² - 3400² = 1135² - 1132² is the difference of 2 nonnegative squares in 2 ways.
6801 is the sum of 2 positive triangular numbers.
6801 is the difference of 2 positive pentagonal numbers in 1 way.
6801 = 1² + 20² + 80² is the sum of 3 positive squares.
6801² is the sum of 3 positive squares.
6801 is a proper divisor of 1153¹¹ - 1.
6801 is an emirpimes in (at least) the following bases: 15, 17, 20, 21, 23, 34, 39, 46, 48, 51, 57, 64, 69, 73, 75, 78, 79, 81, 82, 86, 87, 89, 93, 96, 97, and 98.
6801 is palindromic in (at least) the following bases: 19, 68, 80, -85, and -100.
6801 in base 19 = ifi and consists of only the digits 'f' and 'i'.
6801 in base 47 = 33X and consists of only the digits '3' and 'X'.

The number 6801 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A004126: a(n) = n*(7*n^2 - 1)/6.
A006889: Exponent of least power of 2 having n consecutive 0's in its decimal representation.
A020439: Numbers n such that continued fraction for sqrt(n) has period 100.
A046489: Sum of the first n palindromes (A002113).
A124811: Number of 4-ary Lyndon words of length n with exactly three 1s.
A124814: Triangle of number of 4-ary Lyndon words of length n containing exactly k 1s.
A126587: a(n) = number of integer lattice points inside the right-angle triangle with legs 3n and 4n (and hypotenuse 5n).
A242788: Numbers n such that (n^n-3)/(n-3) is an integer.
A257352: G.f.: (1-2*x+51*x^2)/(1-x)^3.
A260147: G.f.: (1/2) * Sum_{n=-oo..+oo} x^n * (1 + x^n)^n, an even function.