A163280 - OEIS

A163280

Square array read by antidiagonals where column k lists the numbers j whose largest divisor <= sqrt(j) is k.

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

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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 j=k*m where m is either a prime >= j or one of the numbers in row k of A163925. - Franklin T. Adams-Watters, Aug 12 2009

LINKS

Table of n, a(n) for n=1..78.

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

Column k lists the numbers j such that A033676(j)=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