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%I #24 Jan 23 2017 13:10:13
%S 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,
%T 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,
%U 2,4,2,11,3,16,3,6,7,8,5,10
%N 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.
%C 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
%H Peter Kagey, <a href="/A279966/b279966.txt">Table of n, a(n) for n = 1..5000</a>
%e After the first 21 terms, the array looks like this:
%e 1 2 4 5 4 2
%e 1 2 1 5 9
%e 2 5 2 1
%e 2 5 4
%e 2 0
%e 5
%e ...
%e 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.
%e 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.
%e From _Hartmut F. W. Hoft_, Jan 23 2017: (Start)
%e Expanded triangle to the first 13 antidiagonals (as in A279967)
%e .
%e 1 2 4 5 4 2 6 11 3 5 8 10 1
%e 1 2 1 5 9 4 5 10 9 7 5 18
%e 2 5 2 1 3 6 2 1 10 8 2
%e 2 5 4 6 4 8 5 2 7 10
%e 2 0 6 6 1 3 4 6 3
%e 5 0 1 10 6 4 3 5
%e 5 7 2 4 14 16 5
%e 2 4 9 1 3 16
%e 2 0 5 11 2
%e 7 0 2 4
%e 8 4 4
%e 2 9
%e 2
%e (End)
%t (* printing of the triangle is commented out of function a279966[] *)
%t (* support functions are in A279967 *)
%t 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]
%t a279966[13] (* values in first 13 antidiagonals. *)
%t (* _Hartmut F. W. Hoft_, Jan 23 2017 *)
%Y Cf. A279967 for the related sequence which sums prior terms.
%Y Cf. A278436.
%Y Cf. A281533. - _Hartmut F. W. Hoft_, Jan 23 2017
%K nonn,tabl
%O 1,3
%A _Alec Jones_, Dec 24 2016
%E Appended name with phrase as in A279967. - _Hartmut F. W. Hoft_, Jan 23 2017
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