Number of the day: 429

Properties of the number 429:

429 is the 7^th Catalan number.
429 = 3 × 11 × 13 is a sphenic number and squarefree.
429 has 3 distinct prime factors, 8 divisors, 7 antidivisors and 240 totatives.
429 has an emirpimes digit sum 15 in base 10.
429 has a triangular digit sum 15 in base 10.
429 has an oblong digit product 72 in base 10.
429 = 215² - 214² = 73² - 70² = 25² - 14² = 23² - 10² is the difference of 2 nonnegative squares in 4 ways.
429 is the sum of 2 positive triangular numbers.
429 is the difference of 2 positive pentagonal numbers in 1 way.
429 = 2² + 5² + 20² is the sum of 3 positive squares.
429² = 165² + 396² is the sum of 2 positive squares in 1 way.
429² is the sum of 3 positive squares.
429 is a proper divisor of 131² - 1.
429 is palindromic in (at least) the following bases: 32, 38, and -9.
429 in base 8 = 655 and consists of only the digits '5' and '6'.
429 in base 14 = 229 and consists of only the digits '2' and '9'.
429 in base 20 = 119 and consists of only the digits '1' and '9'.

The number 429 belongs to the following On-Line Encyclopedia of Integer Sequences (OEIS) sequences (among others):

Sequence numbers and descriptions below are taken from OEIS.
A000108: Catalan numbers: C(n) = binomial(2n,n)/(n+1) = (2n)!/(n!(n+1)!).
A001790: Numerators in expansion of 1/sqrt(1-x).
A007304: Sphenic numbers: products of 3 distinct primes.
A008593: Multiples of 11.
A009766: Catalan's triangle T(n,k) (read by rows): each term is the sum of the entries above and to the left, i.e., T(n,k) = Sum_{j=0..k} T(n-1,j).
A019565: The squarefree numbers ordered lexicographically by their prime factorization (with factors written in decreasing order). a(n) = Product_{k in I} prime(k+1), where I is the set of indices of nonzero binary digits in n = Sum_{k in I} 2^k.
A033184: Catalan triangle A009766 transposed.
A039598: Triangle formed from odd-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x). Sometimes called Catalan's triangle.
A039599: Triangle formed from even-numbered columns of triangle of expansions of powers of x in terms of Chebyshev polynomials U_n(x).
A089408: Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089864.