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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. 25
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 (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. [From Franklin T. Adams-Watters, Aug 12 2009]

LINKS

Table of n, a(n) for n=1..71.

Omar E. Pol, Illustration of initial terms of column 1: A008578

Omar E. Pol, Illustration of initial terms of column 2: A161344

Omar E. Pol, Illustration of initial terms of columns 1-4: A008578, A161344, A161345, A161424

Index entries for sequences that are permutations of the natural numbers

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,...

2,   6, 12,  20,  30,  42,  56,  72,  90, 110, 132,...

3,   8, 15,  24,  35,  48,  63,  80,  99, 120, 143,...

5,  10, 18,  28,  40,  54,  70,  88, 108, 130, 154,...

7,  14, 21,  32,  45,  60,  77,  96, 117, 140, 165,...

11, 22, 27,  44,  50,  66,  84, 104, 126, 150, 176,...

13, 26, 33,  52,  55,  78,  91, 112, 135, 160, 187,...

17, 34, 39,  68,  65, 102,  98, 128, 153, 170, 198,...

19, 38, 51,  76,  75, 114, 105, 136, 162, 190, 209,...

23, 46, 57,  92,  85, 138, 119, 152, 171, 200, 220,...

29, 58, 69, 116,  95, 174, 133, 184, 189, 230, 231,...

31, 62, 87, 124, 115, 186, 147, 232, 207, 250, 242,...

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: [From R. J. Mathar, Aug 09 2009]

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 A255127 A083221

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

STATUS

approved

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Last modified August 19 07:12 EDT 2017. Contains 290794 sequences.