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A279966
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Square array read by antidiagonals upwards in which each term is the number of prior elements in the same row, column, diagonal, or antidiagonal that divide n; the array is seeded with an initial value a(1)=1.
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6
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1, 1, 2, 2, 2, 4, 2, 5, 1, 5, 2, 5, 2, 5, 4, 5, 0, 4, 1, 9, 2, 5, 0, 6, 6, 3, 4, 6, 2, 7, 1, 6, 4, 6, 5, 11, 2, 4, 2, 10, 1, 8, 2, 10, 3, 7, 0, 9, 4, 6, 3, 5, 1, 9, 5, 8, 0, 5, 1, 14, 4, 4, 2, 10, 7, 8, 2, 4, 2, 11, 3, 16, 3, 6, 7, 8, 5, 10
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OFFSET
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1,3
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COMMENTS
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The patterns of values 2 and 0 in columns 1 and 2, respectively, of the triangle of sequence A279967 do not hold for this sequence, in addition, it appears that every column contains two 1's. - Hartmut F. W. Hoft, Jan 23 2017
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LINKS
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EXAMPLE
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After the first 21 terms, the array looks like this:
1 2 4 5 4 2
1 2 1 5 9
2 5 2 1
2 5 4
2 0
5
...
We have a(20) = 9 because 20 is divisible by a(2) = 1, a(5) = 2, a(9) = 1, a(10) = 5, a(14) = 5, a(15) = 4, a(16) = 5, a(18) = 4, and a(19) = 1.
Likewise, a(17) = 0 because no prior elements of the same row, column, diagonal, or antidiagonal divide 17. See A278436 for a list of indices for which a(n) = 0.
Expanded triangle to the first 13 antidiagonals (as in A279967)
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1 2 4 5 4 2 6 11 3 5 8 10 1
1 2 1 5 9 4 5 10 9 7 5 18
2 5 2 1 3 6 2 1 10 8 2
2 5 4 6 4 8 5 2 7 10
2 0 6 6 1 3 4 6 3
5 0 1 10 6 4 3 5
5 7 2 4 14 16 5
2 4 9 1 3 16
2 0 5 11 2
7 0 2 4
8 4 4
2 9
2
(End)
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MATHEMATICA
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(* printing of the triangle is commented out of function a279966[] *)
(* support functions are in A279967 *)
a279966[k_] := Module[{ut=upperTriangle[k], ms=Table[" ", {i, 1, k}, {j, 1, k}], h, pos, val, seqL={1}}, ms[[1, 1]]=1; For[h=2, h<=Length[ut], h++, pos=ut[[h]]; val=Length[Select[Map[ms[[Apply[Sequence, #]]]&, priorPos[pos]], #!=0 && Mod[seqPos[pos], #]==0&]]; AppendTo[seqL, val]; ms[[Apply[Sequence, pos]]]=val]; (* Print[TableForm[ms]]; *) seqL]
a279966[13] (* values in first 13 antidiagonals. *)
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CROSSREFS
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Cf. A279967 for the related sequence which sums prior terms.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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