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A081312
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Numbers having a unique representation as sum of a prime and an 3-smooth number.
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4
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3, 24, 28, 42, 48, 52, 54, 58, 60, 66, 72, 90, 102, 108, 114, 132, 138, 150, 168, 172, 174, 180, 192, 196, 198, 214, 228, 234, 240, 246, 252, 264, 268, 270, 282, 294, 298, 312, 318, 348, 354, 360, 384, 390, 402, 404, 420, 432, 444, 450, 462, 468, 478, 480, 492
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internal format)
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OFFSET
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1,1
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LINKS
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FORMULA
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MATHEMATICA
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sp3sQ[n_]:=Length[Select[IntegerPartitions[n, {2}], (PrimeQ[#[[1]]]&&Max[ FactorInteger[#[[2]]][[All, 1]]]<4)||(PrimeQ[#[[2]]]&&Max[ FactorInteger[ #[[1]]][[All, 1]]]<4)&]]==1; Select[Range[500], sp3sQ]/.(5->Nothing) (* Harvey P. Dale, Feb 05 2019 *)
nmax = 1000;
S = Select[Range[nmax], Max[FactorInteger[#][[All, 1]]] <= 3 &];
A081308[n_] := Count[TakeWhile[S, # < n &], s_ /; PrimeQ[n - s]];
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PROG
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(Haskell)
a081312 n = a081312_list !! (n-1)
a081312_list = filter ((== 1) . a081308) [1..]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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