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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
OFFSET
1,1
COMMENTS
Conjecture: a(n) > 1 for all n > 0.
LINKS
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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 05 2014
STATUS
approved