A371799 Rectangular array, read by downward antidiagonals: row n shows the numbers m>1 in whose prime factorization p(1)^e(1)*p(2)^e(2)* ...*p(k)^e(k), all e(i) are <= 1 and the number of 0' s in {e(i)} is n-1.
2, 6, 3, 30, 10, 5, 210, 15, 14, 7, 2310, 42, 21, 22, 11, 30030, 70, 35, 33, 26, 13, 510510, 105, 66, 55, 39, 34, 17, 9699690, 330, 110, 77, 65, 51, 38, 19, 223092870, 462, 154, 78, 91, 85, 57, 46, 23, 6469693230, 770, 165, 130, 102, 114, 95, 69, 58, 29
Offset: 1
Examples
15 = 2^0*3^1*51, so (e(1),e(2),e(3)) = (0,1,1), so 15 is in row 2 Corner: 2 6 30 210 2310 30030 510510 9699690 3 10 15 42 70 105 330 462 5 14 21 35 66 110 154 165 7 22 33 55 77 78 130 182 11 26 39 65 91 102 143 170 13 34 51 85 114 119 187 190 17 38 57 95 133 138 209 230 19 46 69 115 161 174 253 290 23 58 87 145 186 203 310 319
Crossrefs
Programs
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Mathematica
exps := Map[#[[2]] &, Sort[Join[#, Complement[Map[{Prime[#], 0} &, Range[PrimePi[Last[#][[1]]]]], Map[{#[[1]], 0} &, #]]]] &[FactorInteger[#]]] &; m = Map[Transpose[#][[1]] &, GatherBy[Map[{#[[1]], Count[#[[2]], 0]} &, Select[Map[{#, exps[#]} &, Range[2, 5000]], Max[#[[2]]] <= 1 &]], #[[2]] &]]; z = 12; row1 = Table[Apply[Times, Prime[Range[n]]], {n, 1, z}]; r = Join[{row1}, Table[Take[m[[n]], z], {n, 2, z}]]; Grid[r] (* array *) w[n_, k_] := r[[n]][[k]] Table[w[n - k + 1, k], {n, z}, {k, n, 1, -1}] // Flatten (* sequence *)(* Peter J. C. Moses, Mar 21 2024 *)