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A049077
a(n) = n / gcd(n, binomial(n, floor(n/2))).
7
1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 1, 1, 7, 1, 8, 1, 9, 1, 5, 1, 11, 1, 6, 1, 13, 1, 7, 1, 1, 1, 16, 1, 17, 1, 3, 1, 19, 1, 2, 1, 7, 1, 11, 1, 23, 1, 4, 1, 25, 1, 13, 1, 27, 1, 1, 1, 29, 1, 15, 1, 31, 1, 32, 1, 11, 1, 17, 1, 5, 1, 18, 1, 37, 1, 19, 1, 39, 1, 4, 1, 41, 1, 1, 1, 43, 1, 11, 1, 1, 1, 23
OFFSET
1,4
LINKS
FORMULA
For odd n, a(n) = 1. For even n, a(n) is either n/2 or smaller.
EXAMPLE
For n = 12, gcd(12, binomial(12, 6)) = gcd(12, 924) = 12, so a(12) = 1.
MAPLE
swing := n -> n!/iquo(n, 2)!^2: seq(n/igcd(n, swing(n)), n=1..92); # Peter Luschny, May 16 2013
MATHEMATICA
Flatten[Table[{1, n/GCD[n, Binomial[n, n/2]]}, {n, 2, 100, 2}]] (* Alonso del Arte, May 17 2013 *)
PROG
(PARI) a(n) = n/gcd(n, binomial(n, n\2)); \\ Michel Marcus, Mar 22 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Nov 13 2000
EXTENSIONS
Offset changed to 1 by Peter Luschny, May 16 2013
STATUS
approved