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.

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

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: A372153 A372170 A369371 * A060465 A219177 A139339

Adjacent sequences: A242204 A242205 A242206 * A242208 A242209 A242210

Keyword

nonn

Author

Zhi-Wei Sun, May 07 2014

Status

approved