A242169 Least prime divisor of Fr(n) which does not divide any Fr(k) with k < n, or 1 if such a primitive prime divisor of Fr(n) does not exist, where Fr(n) denotes the n-th Franel number given by A000172.

2, 5, 7, 173, 563, 13, 41, 369581, 937, 61, 23, 29, 2141, 12148537, 31, 157, 59, 37, 506251, 151, 3019, 769, 47, 6730949, 79, 53, 3853, 661, 138961158000728258971, 1361, 421, 96920594213, 51378681049, 457, 71

Offset: 1

Author

Zhi-Wei Sun, May 05 2014

Keywords

• nonn

Comments

Conjecture: a(n) > 1 for all n > 0.

Examples

			a(7) = 41 since Fr(7) = 2^9*5*41 with the prime factor 41 dividing none of Fr(1), ..., Fr(6) but 2 divides Fr(1) = 2 and 5 divides Fr(2) = 10.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..105

Crossrefs

Cf. A000040, A000172, A242170, A242171, A242173.

Programs

Mathematica

Fr[n_]:=Sum[Binomial[n,k]^3,{k,0,n}]
f[n_]:=FactorInteger[Fr[n]]
p[n_]:=Table[Part[Part[f[n],k],1],{k,1,Length[f[n]]}]
Do[Do[Do[If[Mod[Fr[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]]}];Print[n," ",1];Label[bb];Continue,{n,1,35}]