A393286 Rectangular array, read by descending antidiagonals; row n gives the positions in A006881 of numbers whose least prime divisor is prime(n).

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, 73, 96, 13, 20, 33, 49, 75, 87, 114, 127, 17, 26, 44, 59, 94, 110, 144, 163, 190, 18, 28, 46, 66, 103, 119, 155, 175, 207, 260, 21, 32, 54, 77, 120, 140, 183, 204

Offset

1,2

Comments

Every positive integer is in exactly one row.

Links

Table of n, a(n) for n=1..63.

Example

Corner
    1      2      3      6      7      9     11     13     17     18
    4      5      8     12     14     16     20     26     28     32
   10     15     19     24     30     33     44     46     54     60
   22     27     35     39     49     59     66     77     83     88
   43     55     62     75     94    103    120    131    138    152
   69     73     87    110    119    140    156    166    178    198
   96    114    144    155    183    201    212    233    261    289
  127    163    175    204    226    239    257    291    317    331
  190    207    247    273    285    308    349    390    405    438
  260    305    338    356    391    436    479    498    547    578
  327    364    379    415    460    513    528    583    618    634
  431    449    488    552    611    632    686    732    746    800
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.

Mathematica

t = With[{z = 3000}, Select[Sort[Times @@@ Subsets[Prime[Range[z/2]],
{2}]], # <= z &]]; (* A006881 *)
f[m_] := FactorInteger[m][[1]][[1]]; g = Map[f, t];
u = Table[Flatten[Position[g, Prime[n]]], {n, 1, 12}];
Grid[u]  (* array *)
v[n_, k_] := u[[n]][[k]];
Table[v[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* sequence *)

Crossrefs

Cf. A006881, A338901 (row 1).

Sequence in context: A379649 A240277 A091449 * A100834 A264996 A100826

Adjacent sequences: A393283 A393284 A393285 * A393287 A393288 A393289

Keyword

nonn,tabl

Author

Clark Kimberling, Feb 09 2026

Status

approved