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%I #10 Feb 18 2026 20:02:12
%S 1,2,4,3,5,10,6,8,15,22,7,12,19,27,43,9,14,24,35,55,69,11,16,30,39,62,
%T 73,96,13,20,33,49,75,87,114,127,17,26,44,59,94,110,144,163,190,18,28,
%U 46,66,103,119,155,175,207,260,21,32,54,77,120,140,183,204
%N Rectangular array, read by descending antidiagonals; row n gives the positions in A006881 of numbers whose least prime divisor is prime(n).
%C Every positive integer is in exactly one row.
%e Corner
%e 1 2 3 6 7 9 11 13 17 18
%e 4 5 8 12 14 16 20 26 28 32
%e 10 15 19 24 30 33 44 46 54 60
%e 22 27 35 39 49 59 66 77 83 88
%e 43 55 62 75 94 103 120 131 138 152
%e 69 73 87 110 119 140 156 166 178 198
%e 96 114 144 155 183 201 212 233 261 289
%e 127 163 175 204 226 239 257 291 317 331
%e 190 207 247 273 285 308 349 390 405 438
%e 260 305 338 356 391 436 479 498 547 578
%e 327 364 379 415 460 513 528 583 618 634
%e 431 449 488 552 611 632 686 732 746 800
%e A006881 = (6, 10, 14, 15, 21, 22, 26, 33, 34, 35, 38, 39, 46, 51, 55, ...), in which the numbers with least prime divisor 3=prime(2) are (4, 5, 8, 12,...), which is row 2.
%t t = With[{z = 3000}, Select[Sort[Times @@@ Subsets[Prime[Range[z/2]],
%t {2}]], # <= z &]]; (* A006881 *)
%t f[m_] := FactorInteger[m][[1]][[1]]; g = Map[f, t];
%t u = Table[Flatten[Position[g, Prime[n]]], {n, 1, 12}];
%t Grid[u] (* array *)
%t v[n_, k_] := u[[n]][[k]];
%t Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* sequence *)
%Y Cf. A006881, A338901 (row 1).
%K nonn,tabl
%O 1,2
%A _Clark Kimberling_, Feb 09 2026