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 A163280 Square array read by antidiagonals where the column k lists the numbers n such that their largest divisor <= sqrt(n) equals k. 27
 1, 2, 4, 3, 6, 9, 5, 8, 12, 16, 7, 10, 15, 20, 25, 11, 14, 18, 24, 30, 36, 13, 22, 21, 28, 35, 42, 49, 17, 26, 27, 32, 40, 48, 56, 64, 19, 34, 33, 44, 45, 54, 63, 72, 81, 23, 38, 39, 52, 50, 60, 70, 80, 90, 100, 29, 46, 51, 68, 55, 66, 77, 88, 99, 110, 121, 31, 58, 57, 76, 65, 78, 84, 96, 108, 120, 132, 144 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence is a permutation of the natural numbers A000027. Note that the first column is formed by 1 together with the prime numbers. Column k contains exactly those numbers k*m where m is either a prime >= n or one of the numbers in row k of A163925. - Franklin T. Adams-Watters, Aug 12 2009 LINKS Omar E. Pol, Illustration of initial terms of column 1: A008578 Omar E. Pol, Illustration of initial terms of column 2: A161344 FORMULA The column k lists the numbers n such that A033676(n)=k. EXAMPLE Array begins:    1,  4,  9,  16,  25,  36,  49,  64,  81, 100, 121, 144, ...    2,  6, 12,  20,  30,  42,  56,  72,  90, 110, 132, 156, ...    3,  8, 15,  24,  35,  48,  63,  80,  99, 120, 143, 168, ...    5, 10, 18,  28,  40,  54,  70,  88, 108, 130, 154, 180, ...    7, 14, 21,  32,  45,  60,  77,  96, 117, 140, 165, 192, ...   11, 22, 27,  44,  50,  66,  84, 104, 126, 150, 176, 204, ...   13, 26, 33,  52,  55,  78,  91, 112, 135, 160, 187, 216, ...   17, 34, 39,  68,  65, 102,  98, 128, 153, 170, 198, 228, ...   19, 38, 51,  76,  75, 114, 105, 136, 162, 190, 209, 264, ...   23, 46, 57,  92,  85, 138, 119, 152, 171, 200, 220, 276, ...   29, 58, 69, 116,  95, 174, 133, 184, 189, 230, 231, 348, ...   31, 62, 87, 124, 115, 186, 147, 232, 207, 250, 242, 372, ...   ... MAPLE A163280 := proc(n, k) local r, T ; r := 0 ; for T from k^2 by k do if A033676(T) = k then r := r+1 ; if r = n then RETURN(T) ; fi; fi; od: end: # R. J. Mathar, Aug 09 2009 MATHEMATICA nmax = 12; pm = Prime[nmax]; sDiv[n_] := Select[Divisors[n], #^2 <= n&][[-1]]; Clear[col]; col[k_] := col[k] = Select[Range[k pm], sDiv[#] == k&]; T[n_, k_ /; 1 <= k <= Length[col[k]]] := col[k][[n]]; Table[T[n-k+1, k], {n, 1, nmax}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 15 2019 *) CROSSREFS Rows 1-12: A000290, A002378, A005563, A164004, A100451, A164006, A164007, A164008, A164009, A164010, A164011, A164012. Columns 1-12: A008578, A161344, A161345, A161424, A161835, A162526, A162527, A162528, A162529, A162530, A162531, A162532. Another version: A163990. Cf. A000027, A000040, A033676, A147861, A163100, A164000. Sequence in context: A179216 A192176 A191711 * A056537 A293054 A255127 Adjacent sequences:  A163277 A163278 A163279 * A163281 A163282 A163283 KEYWORD nonn,tabl AUTHOR Omar E. Pol, Aug 07 2009 EXTENSIONS Edited by R. J. Mathar, Aug 01 2010 Example edited by Jean-François Alcover, Dec 15 2019 STATUS approved

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Last modified July 29 04:52 EDT 2021. Contains 346340 sequences. (Running on oeis4.)