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.
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
Offset: 1
Examples
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)
Links
- Peter Kagey, Table of n, a(n) for n = 1..5000
Crossrefs
Cf. A279967 for the related sequence which sums prior terms.
Cf. A278436.
Cf. A281533. - Hartmut F. W. Hoft, Jan 23 2017
Programs
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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 *)
Extensions
Appended name with phrase as in A279967. - Hartmut F. W. Hoft, Jan 23 2017
Comments