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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 05 2014
STATUS
approved