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 A242207 Least prime divisor of the n-th Domb number D(n) which does not divide any D(k) with k < n, or 1 if such a primitive prime divisor of D(n) does not exist. 4

%I

%S 2,7,1,97,11,23,19,643,659,1753,4922329,613,341447,1193,2213,

%T 2040452101603,491,82461839,733,113,1108394340978316050481,

%U 1034497328556150923437,593,73,17117,804943,422291,1559,858631,337655751557

%N Least prime divisor of the n-th Domb number D(n) which does not divide any D(k) with k < n, or 1 if such a primitive prime divisor of D(n) does not exist.

%C Conjecture: a(n) is prime except for n = 3.

%H Zhi-Wei Sun, <a href="/A242207/b242207.txt">Table of n, a(n) for n = 1..72</a>

%e a(4) = 97 since D(4) = 2^2*7*97 with 97 dividing none of D(1) = 2^2, D(2) = 2^2*7 and D(3) = 2^8.

%t d[n_]:=Sum[Binomial[n,k]^2*Binomial[2k,k]*Binomial[2(n-k),n-k],{k,0,n}]

%t f[n_]:=FactorInteger[d[n]]

%t p[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]

%t Do[If[d[n]<2,Goto[cc]];Do[Do[If[Mod[d[i],Part[p[n],k]]==0,Goto[aa]],{i,1,n-1}];Print[n," ",Part[p[n],k]];Goto[bb];Label[aa];Continue,{k,1,Length[p[n]]}];Label[cc];Print[n," ",1];Label[bb];Continue,{n,1,30}]

%Y Cf. A000040, A002895, A242169, A242170, A242171, A242173, A242174, A242193, A242194, A242195.

%K nonn

%O 1,1

%A _Zhi-Wei Sun_, May 07 2014

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Last modified December 10 23:18 EST 2019. Contains 329910 sequences. (Running on oeis4.)