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A242207 Least prime divisor of the n-th Domb 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. 4
2, 7, 1, 97, 11, 23, 19, 643, 659, 1753, 4922329, 613, 341447, 1193, 2213, 2040452101603, 491, 82461839, 733, 113, 1108394340978316050481, 1034497328556150923437, 593, 73, 17117, 804943, 422291, 1559, 858631, 337655751557 (list; graph; refs; listen; history; text; internal format)
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

Cf. A000040, A002895, A242169, A242170, A242171, A242173, A242174, A242193, A242194, A242195.

Sequence in context: A261390 A248676 A125699 * A060465 A219177 A139339

Adjacent sequences:  A242204 A242205 A242206 * A242208 A242209 A242210

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, May 07 2014

STATUS

approved

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Last modified November 15 01:25 EST 2019. Contains 329143 sequences. (Running on oeis4.)