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A305996
Rectangular array, by antidiagonals; row n consists of the numbers R(n)/n, where R(n) is row n of the array at A305995.
2
1, 10, 1, 65, 34, 1, 130, 260, 2, 1, 260, 884, 5, 10, 1, 340, 1300, 10, 26, 10, 2, 1105, 3380, 20, 260, 340, 20, 1, 1972, 8840, 50, 5140, 650, 52, 2, 1, 2210, 31300, 65, 8840, 1565, 100, 5, 260, 1, 4420, 82948, 68, 21320, 5525, 520, 10, 514, 2, 2
OFFSET
1,2
EXAMPLE
Northwest corner:
1 10 65 130 260 340 1105
1 34 260 884 1300 3380 8840
1 2 5 10 20 50 65
1 10 26 260 5140 8840 21430
1 10 340 650 1565 5525 6260
2 30 52 100 520 10280 17680
1 2 5 10 20 25 50
MATHEMATICA
z = 3000; r[n_] := Select[Divisors[n], GCD[#, n/#] == 1 &]; k[n_] := Length[r[n]];
t[n_] := Table[r[n][[k[n] + 1 - i]]/r[n][[k[1] + i - 1]], {i, 1, k[n]}];
s = Table[Plus @@ t[n], {n, 1, z}];
a[n_] := If[IntegerQ[s[[n]]], 1, 0];
u = Table[a[n], {n, 1, z}]; (*A229996*)
d = Denominator[s]; row[n_] := Flatten[Position[d, n]] (*A305995 array*)
rr[n_] := row[n]/n;
TableForm[Table[rr[n], {n, 1, 100}]] (* A305996 array *)
r1[n_, k_] := rr[n][[k]];
Flatten[Table[r1[n - k + 1, k], {n, 5}, {k, n, 1, -1}]] (* A305996 sequence *)
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jun 16 2018
STATUS
approved