cp's OEIS Frontend

A080170 Numbers k such that gcd(C(2*k,k), C(3*k,k), C(4*k,k), ..., C((k+1)*k,k) ) = 1.

%I A080170 #17 Feb 28 2020 01:27:23
%S A080170 29,59,69,83,89,104,119,125,131,139,153,164,167,179,181,194,197,209,
%T A080170 219,230,233,251,259,263,272,279,285,305,307,311,314,329,335,339,356,
%U A080170 359,363,373,379,384,389,395,398,407,417,419,428,439,441,454,455,461
%N A080170 Numbers k such that gcd(C(2*k,k), C(3*k,k), C(4*k,k), ..., C((k+1)*k,k) ) = 1.
%C A080170 a(n) = A051283(n) - 1 (conjectured). - _Ralf Stephan_, Feb 20 2004
%t A080170 Select[Range[500], GCD@@Table[Binomial[k*#, # ], {k, 2, #+1}]==1&]
%o A080170 (Haskell)
%o A080170 a080170 n = a080170_list !! (n-1)
%o A080170 a080170_list = filter f [1..] where
%o A080170    f x = foldl1 gcd (map (flip a007318' x) [2*x, 3*x .. x*(x+1)]) == 1
%o A080170 -- _Reinhard Zumkeller_, May 30 2013
%o A080170 (PARI) isok(k) = gcd(vector(k, i, binomial(k+i*k,k))) == 1; \\ _Jinyuan Wang_, Feb 28 2020
%Y A080170 Cf. A007318, A051283.
%K A080170 nonn
%O A080170 1,1
%A A080170 _Benoit Cloitre_, Jan 31 2003