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A285090 Rectangular array by antidiagonals: the array formed by arranging the rows of A285089 so that the first column is strictly increasing.

%I A285090 #4 Apr 14 2017 03:59:28
%S A285090 1,4,2,9,6,3,16,12,8,5,25,20,15,21,7,36,30,24,32,27,10,49,42,35,45,55,
%T A285090 18,11,64,56,48,60,91,28,39,13,81,72,63,77,112,40,75,85,14,100,90,80,
%U A285090 96,135,54,119,133,50,17,121,110,99,117,160,70,171,189,66
%N A285090 Rectangular array by antidiagonals: the array formed by arranging the rows of A285089 so that the first column is strictly increasing.
%C A285090 Every positive integer occurs exactly once, so that as a sequence, this is a permutation of the natural numbers, A000027.  Every prime (A000040) occurs in column 1.  For each row, there is a nonnegative integer h such that all but finitely many initial entries are of the form k*(k+h).
%H A285090 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e A285090 Northwest corner:
%e A285090 1   4   9    16   25   36   49   64   81   10
%e A285090 2   6   12   20   30   42   56   72   90   110
%e A285090 3   8   15   24   35   48   63   80   99   120
%e A285090 5   21  32   45   60   77   96   117  140  165
%e A285090 7   27  55   91   112  135  160  187  216  247
%e A285090 10  18  28   40   54   70   88   108  130  154
%e A285090 11  39  75   119  171  200  231  264  299  375
%e A285090 13  85  133  189  253  325  364  405  448  493
%t A285090 d[n_] := Divisors[n]; k[n_] := Length[d[n]]; x[n_, i_] := d[n][[i]];
%t A285090 a[n_] := If[OddQ[k[n]], 0, x[n, k[n]/2 + 1] - x[n, k[n]/2]]
%t A285090 t = Table[a[j], {j, 1, 30000}];
%t A285090 r[n_] := Flatten[Position[t, n]]; v[n_, k_] := r[n][[k]];
%t A285090 w = Table[v[n, k], {n, 0, 20}, {k, 1, 20}];
%t A285090 y = SortBy[w, First]; v[n_, k_] := y[[n, k]];
%t A285090 w = TableForm[Table[v[n, k], {n, 1, 10}, {k, 1, 10}]]
%t A285090 Table[v[n + 1 - k, k], {n, 1, 15}, {k, n, 1, -1}] // Flatten
%Y A285090 Cf. A000027, A000040, A000290, A095833, A163280, A285089.
%K A285090 nonn,tabl,easy
%O A285090 1,2
%A A285090 _Clark Kimberling_, Apr 13 2017