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A279966 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.

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