OFFSET
1,1
COMMENTS
Conjecture: a(n) is prime except for n = 3.
LINKS
Zhi-Wei Sun, Table of n, a(n) for n = 1..72
EXAMPLE
a(4) = 97 since D(4) = 2^2*7*97 with 97 dividing none of D(1) = 2^2, D(2) = 2^2*7 and D(3) = 2^8.
MATHEMATICA
d[n_]:=Sum[Binomial[n, k]^2*Binomial[2k, k]*Binomial[2(n-k), n-k], {k, 0, n}]
f[n_]:=FactorInteger[d[n]]
p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[d[n]<2, Goto[cc]]; Do[Do[If[Mod[d[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]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 07 2014
STATUS
approved