A305996 - OEIS

%I #6 Jun 17 2018 09:47:09

%S 1,10,1,65,34,1,130,260,2,1,260,884,5,10,1,340,1300,10,26,10,2,1105,

%T 3380,20,260,340,20,1,1972,8840,50,5140,650,52,2,1,2210,31300,65,8840,

%U 1565,100,5,260,1,4420,82948,68,21320,5525,520,10,514,2,2

%N Rectangular array, by antidiagonals; row n consists of the numbers R(n)/n, where R(n) is row n of the array at A305995.

%e Northwest corner:

%e   1  10   65  130   260    340   1105

%e   1  34  260  884  1300   3380   8840

%e   1   2    5   10    20     50     65

%e   1  10   26  260  5140   8840  21430

%e   1  10  340  650  1565   5525   6260

%e   2  30   52  100   520  10280  17680

%e   1   2    5   10    20     25     50

%t z = 3000; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; k[n_] := Length[r[n]];

%t t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];

%t s = Table[Plus @@ t[n], {n, 1, z}];

%t a[n_] := If[IntegerQ[s[[n]]], 1, 0];

%t u = Table[a[n], {n, 1, z}]; (*A229996*)

%t d = Denominator[s]; row[n_] := Flatten[Position[d, n]] (*A305995 array*)

%t rr[n_] := row[n]/n;

%t TableForm[Table[rr[n], {n, 1, 100}]] (* A305996 array *)

%t r1[n_, k_] := rr[n][[k]];

%t Flatten[Table[r1[n - k + 1, k], {n, 5}, {k, n, 1, -1}]]  (* A305996 sequence *)

%Y Cf. A077610, A229994, A229996, A229997, A229998, A229998, A305995.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Jun 16 2018