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A348824
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Numbers in array A327259 that do not have a unique decomposition into numbers of A327261.
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1
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32, 48, 72, 96, 112, 126, 128, 144, 160, 168, 176, 192, 198, 221, 224, 240, 252, 256, 264, 288, 294, 304, 336, 342, 347, 352, 360, 368, 384, 392, 396, 414, 416, 432, 448, 456, 462, 480, 496, 504, 512, 528, 544, 545, 552, 558, 560, 576, 588, 599
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OFFSET
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1,1
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COMMENTS
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While array A327259 has many properties of the multiplication table, one way the numbers that sieve out of the array fail to be prime numbers is that unique factorization does not hold. Some numbers have two or more decompositions.
For i >= 2, A327259(i, a(n)) is in the sequence.
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LINKS
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EXAMPLE
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The first six terms and their decompositions:
More in a-file.
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MATHEMATICA
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T[n_, k_]:=2n*k-If[Mod[n, 2]==1, If[Mod[k, 2]==1, n+k-1, k], If[Mod[k, 2]==1, n, 0]]; F[d_]:=If[(q=Union[Sort/@(Position[Table[T[n, k], {n, 2, Ceiling[d/3]}, {k, 2, Ceiling[d/3]}], d]+1)])=={}, {{d}}, q]; FC[x_]:=FixedPoint[Union[Sort/@Flatten[Flatten/@Tuples[#]&/@((F/@#&/@#)&[#]), 1]]&, F[x]]; list={}; Do[If[Length@FC@i>1, AppendTo[list, i]], {i, 300}]; list (* Giorgos Kalogeropoulos, Nov 05 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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