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

1,1

Comments

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

Links

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

Example

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.

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}]

Crossrefs

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

Sequence in context: A041445 A265815 A041961 * A058854 A006275 A042673

Adjacent sequences: A242166 A242167 A242168 * A242170 A242171 A242172

Keyword

nonn

Author

Zhi-Wei Sun, May 05 2014

Status

approved