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A242173
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Least prime divisor of the n-th central Delannoy number D(n) which does not divide any D(k) with k < n, or 1 if such a primitive prime divisor of D(n) does not exist.
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11
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3, 13, 7, 107, 11, 89, 31, 265729, 19, 9887, 23, 113, 79, 373, 53, 3089, 151, 127, 719, 193, 43, 482673878761, 47, 61403, 109, 37889, 1223, 3251609, 59, 181, 22504880485262968151, 3598831, 67, 69593, 179, 13828116559, 4247285503, 1579, 19095283759, 619
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OFFSET
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1,1
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COMMENTS
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Conjecture:
(i) a(n) > 1 for all n > 0.
(ii) For any integer n > 0, the n-th Apéry number A(n) = Sum_{k=0..n} (binomial(n,k)*binomial(n+k,k))^2 has a prime divisor which does not divide any A(k) with k < n.
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LINKS
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EXAMPLE
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a(3) = 7 since D(3) = 3^2*7 with 7 dividing none of D(1) = 3 and D(2) = 13.
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MATHEMATICA
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d[n_]:=Sum[Binomial[n+k, k]*Binomial[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, 40}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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