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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. 6
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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

LINKS

Peter Kagey, Table of n, a(n) for n = 1..5000

EXAMPLE

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.

From Hartmut F. W. Hoft, Jan 23 2017: (Start)

Expanded triangle to the first 13 antidiagonals  (as in A279967)

.

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)

MATHEMATICA

(* 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. *)

(* Hartmut F. W. Hoft, Jan 23 2017 *)

CROSSREFS

Cf. A279967 for the related sequence which sums prior terms.

Cf. A278436.

Cf. A281533. - Hartmut F. W. Hoft, Jan 23 2017

Sequence in context: A098069 A173738 A135838 * A114349 A186749 A133265

Adjacent sequences:  A279963 A279964 A279965 * A279967 A279968 A279969

KEYWORD

nonn,tabl

AUTHOR

Alec Jones, Dec 24 2016

EXTENSIONS

Appended name with phrase as in A279967. - Hartmut F. W. Hoft, Jan 23 2017

STATUS

approved

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Last modified May 28 12:02 EDT 2020. Contains 334681 sequences. (Running on oeis4.)