The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056059 GCD of largest square and squarefree part of central binomial coefficients. 9
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 3, 6, 2, 1, 1, 1, 3, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 6, 3, 1, 1, 1, 2, 3, 6, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 3, 6, 6, 3, 1, 2, 2, 1, 2, 1, 3, 6, 1, 1, 1, 2, 1, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,14 LINKS Antti Karttunen, Table of n, a(n) for n = 1..10000 FORMULA a(n) = A055229(A001405(n)), where A055229(n) = gcd(A008833(n), A007913(n)). EXAMPLE n=14, binomial(14,7) = 3432 = 8*3*11*13. The largest square divisor is 4, squarefree part is 858. So a(14) = gcd(4,858) = 2. MATHEMATICA Table[GCD[First@ Select[Reverse@ Divisors@ #, IntegerQ@ Sqrt@ # &], Times @@ Power @@@ Map[{#1, Mod[#2, 2]} & @@ # &, FactorInteger@ #]] &@ Binomial[n, Floor[n/2]], {n, 80}] (* Michael De Vlieger, Feb 18 2017, after Zak Seidov at A007913 *) PROG (PARI) A001405(n) = binomial(n, n\2); A055229(n) = { my(c=core(n)); gcd(c, n/c); } \\ Charles R Greathouse IV, Nov 20 2012 A056059(n) = A055229(A001405(n)); \\ Antti Karttunen, Jul 20 2017 (Python) from sympy import binomial, gcd, floor from sympy.ntheory.factor_ import core def a001405(n): return binomial(n, floor(n/2)) def a055229(n):     c=core(n)     return gcd(c, n/c) def a(n): return a055229(a001405(n)) print map(a, range(1, 151)) # Indranil Ghosh, Jul 20 2017 CROSSREFS Cf. A000188, A001405, A007913, A008833, A034974, A046098, A055229, A055231. Cf. A056056, A056057, A056058, A056060, A056061. Sequence in context: A238015 A257679 A031214 * A158819 A031279 A124778 Adjacent sequences:  A056056 A056057 A056058 * A056060 A056061 A056062 KEYWORD nonn AUTHOR Labos Elemer, Jul 26 2000 EXTENSIONS Formula clarified by Antti Karttunen, Jul 20 2017 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 23 16:14 EST 2020. Contains 332173 sequences. (Running on oeis4.)