A242174 Least prime divisor of A005260(n) which does not divide any previous term A005260(k) with k < n, or 1 if such a primitive prime divisor of A005260(n) does not exist.

2, 3, 41, 5, 7, 349, 61, 75617, 31, 13, 499, 643897693, 17, 19, 1729774061, 101, 2859112064587, 138407, 83, 167, 59, 29, 653, 257, 997540809461453561581, 347, 13679, 37, 160449179727717672892660463, 211, 151, 43, 97, 73, 47

Offset: 1

Author

Zhi-Wei Sun, May 07 2014

Keywords

• nonn

Comments

Conjecture: a(n) is prime for any n > 0. In general, for any r > 2, if n is large enough then f_r(n) = sum_{k=0..n}C(n,k)^r has a prime divisor which does not divide any previous terms f_r(k) with k < n.

Examples

			a(3) = 41 since A005260(3) = 2^2*41 with 41 dividing none of A005260(1) = 2 and A005260(2) = 2*3^2.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..82

Crossrefs

Cf. A000040, A005260, A242169, A242170, A242171, A242173, A242193, A242194, A242195, A242207.

Programs

Mathematica

u[n_]:=Sum[Binomial[n,k]^4,{k,0,n}]
f[n_]:=FactorInteger[u[n]]
p[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]
Do[If[u[n]<2,Goto[cc]];Do[Do[If[Mod[u[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,1,35}]