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A242180
Least prime divisor of q(n) which does not divide any q(k) with k < n, or 1 if such a primitive prime divisor does not exist, where q(.) is the strict partition function given by A000009.
1
1, 1, 2, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 11, 1, 1, 19, 23, 1, 1, 1, 89, 13, 61, 71, 1, 1, 37, 1, 1, 17, 1, 7, 1, 1, 167, 1, 1, 491, 53, 1, 31, 1, 227, 1, 1, 1, 97, 1, 59, 241, 29, 1, 953, 1063, 1777, 1, 367, 1, 1
OFFSET
1,3
COMMENTS
Conjecture: a(n) > 1 for all n > 203.
EXAMPLE
a(8) = 1 since q(8) = 2*3 with 2 = q(3) and 3 = q(5).
a(23) = 13 since q(23) = 2^3*13 with 13 not dividing q(1)*q(2)*...*q(22), but 2 divides q(3) = 2.
MATHEMATICA
f[n_]:=FactorInteger[PartitionsQ[n]]
pp[n_]:=Table[Part[Part[f[n], k], 1], {k, 1, Length[f[n]]}]
Do[If[PartitionsQ[n]<2, Goto[cc]]; Do[Do[If[Mod[PartitionsQ[i], Part[pp[n], k]]==0, Goto[aa]], {i, 1, n-1}]; Print[n, " ", Part[pp[n], k]]; Goto[bb]; Label[aa]; Continue, {k, 1, Length[pp[n]]}]; Label[cc]; Print[n, " ", 1]; Label[bb]; Continue, {n, 1, 60}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, May 06 2014
STATUS
approved