Number of the day: 4220

Adrien-Marie Legendre was born on this day 268 years ago.

Properties of the number 4220:

4220 is the 1074^th totient number.
4220 = 2² × 5 × 211 is the 3641^th composite number and is not squarefree.
4220 has 3 distinct prime factors, 12 divisors, 11 antidivisors and 1680 totatives.
4220 has a Fibonacci digit sum 8 in base 10.
4220 = 1056² - 1054² = 216² - 206² is the difference of 2 nonnegative squares in 2 ways.
4220 is the difference of 2 positive pentagonal numbers in 2 ways.
4220 is not the sum of 3 positive squares.
4220² = 2532² + 3376² is the sum of 2 positive squares in 1 way.
4220² is the sum of 3 positive squares.
4220 is a proper divisor of 421² - 1.
4220 = '42' + '20' is the concatenation of 2 oblong numbers.
4220 is palindromic in (at least) the following bases: 31, 38, -34, and -57.
4220 in base 24 = 77k and consists of only the digits '7' and 'k'.
4220 in base 26 = 668 and consists of only the digits '6' and '8'.
4220 in base 30 = 4kk and consists of only the digits '4' and 'k'.
4220 in base 31 = 4c4 and consists of only the digits '4' and 'c'.
4220 in base 37 = 332 and consists of only the digits '2' and '3'.
4220 in base 38 = 2Z2 and consists of only the digits '2' and 'Z'.

The number 4220 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A028931: Strings giving winning positions in Tchoukaillon (or Mancala) solitaire.
A077588: Maximum number of regions into which the plane is divided by n triangles.
A108643: Number of binary rooted trees with n nodes and internal path length n.
A124353: Number of (directed) Hamiltonian circuits on the n-antiprism graph.
A134212: Positions of 12 after decimal point in decimal expansion of Pi.
A205590: T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no 2X2 subblock having the same number of equal edges as its horizontal or vertical neighbors, and new values 0..2 introduced in row major order.
A276550: Array read by antidiagonals: T(n,k) = number of primitive (period n) bracelets using a maximum of k different colored beads.
A283726: T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than two of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
A325583: G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * ((1 + 3*x)^n - A(x))^(n+1), where A(0) = 0.
A333139: The number of regions inside a decagon formed by the straight line segments mutually connecting all vertices and all points that divide the sides into n equal parts.