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