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 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. 11
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified June 22 01:32 EDT 2021. Contains 345367 sequences. (Running on oeis4.)