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.

2, 7, 1, 97, 11, 23, 19, 643, 659, 1753, 4922329, 613, 341447, 1193, 2213, 2040452101603, 491, 82461839, 733, 113, 1108394340978316050481, 1034497328556150923437, 593, 73, 17117, 804943, 422291, 1559, 858631, 337655751557

Offset: 1

Author

Zhi-Wei Sun, May 07 2014

Keywords

• nonn

Comments

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

Examples

			 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.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..72

Crossrefs

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

Programs

Mathematica

d[n_]:=Sum[Binomial[n,k]^2*Binomial[2k,k]*Binomial[2(n-k),n-k],{k,0,n}]
f[n_]:=FactorInteger[d[n]]
p[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]
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}]