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A194262
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Largest prime that divides the n-th partition number p(n) but does not divide p(1)*p(2)*...*p(n-1), or 1 if none.
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4
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1, 2, 3, 5, 7, 11, 1, 1, 1, 1, 1, 1, 101, 1, 1, 1, 1, 1, 1, 19, 1, 167, 251, 1, 89, 29, 43, 13, 83, 467, 311, 23, 1, 1231, 41, 17977, 281, 1, 1, 127, 193, 2417, 71, 97, 1087, 241, 67, 7013, 631, 9283, 661, 53, 5237, 59, 227, 1019, 102359, 3251, 199, 409, 971
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OFFSET
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1,2
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COMMENTS
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It appears that a(n) is prime for all n > 97. See A194259 and A194260 for additional comments and links.
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LINKS
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MAPLE
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with(combinat): with(numtheory):
b:= proc(n) option remember;
`if`(n=1, {}, b(n-1) union factorset(numbpart(n)))
end:
a:= n-> `if`(n=1, 1, max(1, (b(n) minus b(n-1))[])):
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MATHEMATICA
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a[n_] := Complement[FactorInteger[PartitionsP[n]][[All, 1]], FactorInteger[Product[PartitionsP[k], {k, 1, n-1}]][[All, 1]]] /. {} -> {1} // Last; Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Jan 28 2014 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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