A071416 a(n) = gcd(n, binomial(2*n, n)).

1, 2, 1, 2, 1, 6, 1, 2, 1, 2, 1, 4, 1, 2, 15, 2, 1, 6, 1, 20, 3, 2, 1, 12, 1, 2, 1, 28, 1, 2, 1, 2, 3, 2, 7, 4, 1, 2, 1, 20, 1, 42, 1, 4, 45, 2, 1, 12, 1, 2, 3, 4, 1, 6, 1, 8, 3, 2, 1, 12, 1, 2, 3, 2, 5, 66, 1, 4, 3, 10, 1, 36, 1, 2, 15, 4, 77, 6, 1, 20, 1, 2, 1, 28, 5, 2, 3, 88, 1, 10, 91, 4, 1, 2, 5

Offset

1,2

Comments

a(n) = n for n in A014847. - Reinhard Zumkeller

a(n) = gcd(n, C(n)), C(n) the Catalan numbers. - Peter Luschny Oct 06 2011

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Central Binomial Coefficient

Example

a(10) = gcd(10, binomial(20, 10)) = gcd(10, 184756) = 2.

Mathematica

Table[GCD[n, Binomial[2n, n]], {n, 100}] (* Harvey P. Dale, Nov 10 2011 *)

Prog

(Python)
from math import prod
from sympy import factorint
from sympy.ntheory.factor_ import digits
def A071416(n):
    f = factorint(n)
    def s(n, p): return sum(digits(n, p)[1:])
    return prod(p**min(f[p], ((s(n, p)<<1)-s(n<<1, p))//(p-1)) for p in f) # Chai Wah Wu, May 05 2026

Crossrefs

Cf. A000984, A000108.

Sequence in context: A337395 A126083 A356158 * A053589 A055770 A225821

Adjacent sequences: A071413 A071414 A071415 * A071417 A071418 A071419

Keyword

nonn,nice

Author

Reinhard Zumkeller, May 29 2002

Status

approved