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%I #17 Feb 28 2020 01:27:23
%S 29,59,69,83,89,104,119,125,131,139,153,164,167,179,181,194,197,209,
%T 219,230,233,251,259,263,272,279,285,305,307,311,314,329,335,339,356,
%U 359,363,373,379,384,389,395,398,407,417,419,428,439,441,454,455,461
%N Numbers k such that gcd(C(2*k,k), C(3*k,k), C(4*k,k), ..., C((k+1)*k,k) ) = 1.
%C a(n) = A051283(n) - 1 (conjectured). - _Ralf Stephan_, Feb 20 2004
%t Select[Range[500], GCD@@Table[Binomial[k*#, # ], {k, 2, #+1}]==1&]
%o (Haskell)
%o a080170 n = a080170_list !! (n-1)
%o a080170_list = filter f [1..] where
%o f x = foldl1 gcd (map (flip a007318' x) [2*x, 3*x .. x*(x+1)]) == 1
%o -- _Reinhard Zumkeller_, May 30 2013
%o (PARI) isok(k) = gcd(vector(k, i, binomial(k+i*k,k))) == 1; \\ _Jinyuan Wang_, Feb 28 2020
%Y Cf. A007318, A051283.
%K nonn
%O 1,1
%A _Benoit Cloitre_, Jan 31 2003