

A242170


Least prime divisor of T(n) which does not divide any T(k) with k < n, or 1 if such a primitive prime divisor of T(n) does not exist, where T(n) is the nth central trinomial coefficient given by A002426.


11



1, 3, 7, 19, 17, 47, 131, 41, 43, 1279, 503, 113, 2917, 569, 198623, 14083, 26693, 201611, 42998951, 41931041, 52635749, 1296973, 169097, 1451, 1304394227, 107, 233, 173, 2062225210273, 719, 191, 31551555041, 6301, 563, 3769, 967, 9539, 5073466546857451, 4542977, 9739
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OFFSET

1,2


COMMENTS

Conjecture: (i) a(n) > 1 for all n > 1.
(ii) For any integer n > 3, the nth Motzkin number M(n) given by A001006 has a prime divisor which does not divide any M(k) with k < n.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..168


EXAMPLE

a(11) = 503 since T(11) = 3*17*503 with the prime divisor 503 dividing none of T(1),...,T(10), but 3 divides T(2) = 3 and 17 divides T(5) = 51.


MATHEMATICA

T[n_]:=Sum[Binomial[n, 2k]*Binomial[2k, k], {k, 0, n/2}]
f[n_]:=FactorInteger[T[n]]
p[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[T[n]<2, Goto[cc]]; Do[Do[If[Mod[T[i], Part[p[n], k]]==0, Goto[aa]], {i, 1, n1}];
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}]


CROSSREFS

Cf. A000040, A001006, A002426, A242169, A242171, A242173.
Sequence in context: A075609 A083439 A151858 * A032675 A089749 A032667
Adjacent sequences: A242167 A242168 A242169 * A242171 A242172 A242173


KEYWORD

nonn


AUTHOR

ZhiWei Sun, May 05 2014


STATUS

approved



