1,2

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 (FrankTAW(AT)Netscape.net), Aug 12 2009]

See also the array in A163990. [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]

O. E. Pol, Determinacion geometrica de los numeros primos y perfectos

O. E. Pol, Illustration: Divisors and pi(x)

O. E. Pol, Illustration for A008578, the first column of the array [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]

O. E. Pol, Illustration for A161344, the second column of the array [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]

O. E. Pol, Illustration for A008578, A161344, A161345 and A161424 [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]

Index entries for sequences that are permutations of the natural numbers [From Omar E. Pol (info(AT)polprimos.com), Oct 25 2009]

The column k lists the numbers n such that A033676(n)=k.

The table begins:

==========================================================================

..... Column k: 1 .. 2 .. 3 .. 4 .. 5 .. 6 .. 7 .. 8 .. 9 . 10 . 11 . 12

==========================================================================

............... A .. A .. A .. A .. A .. A .. A .. A .. A .. A .. A .. A .

............... 0 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .. 1 .

............... 0 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .. 6 .

............... 8 .. 1 .. 1 .. 1 .. 1 .. 2 .. 2 .. 2 .. 2 .. 2 .. 2 .. 2 .

............... 5 .. 3 .. 3 .. 4 .. 8 .. 5 .. 5 .. 5 .. 5 .. 5 .. 5 .. 5 .

............... 7 .. 4 .. 4 .. 2 .. 3 .. 2 .. 2 .. 2 .. 2 .. 3 .. 3 .. 3 .

Row ........... 8 .. 4 .. 5 .. 4 .. 5 .. 6 .. 7 .. 8 .. 9 .. 0 .. 1 .. 2 .

==========================================================================

.1 : A000290: ..1, ..4, ..9, .16, .25, .36, .49, .64, .81, 100, 121, 144,

.2 : A002378: ..2, ..6, .12, .20, .30, .42, .56, .72, .90, 110, 132, 156,

.3 : .......: ..3, ..8, .15, .24, .35, .48, .63, .80, .99, 120, 143, 168,

.4 : A164004: ..5, .10, .18, .28, .40, .54, .70, .88, 108, 130, 154, 180,

.5 : .......: ..7, .14, .21, .32, .45, .60, .77, .96, 117, 140, 165, 192,

.6 : A164006: .11, .22, .27, .44, .50, .66, .84, 104, 126, 150, 176, 204,

.7 : A164007: .13, .26, .33, .52, .55, .78, .91, 112, 135, 160, 187, 216,

.8 : A164008: .17, .34, .39, .68, .65, 102, .98, 128, 153, 170, 198, 228,

.9 : A164009: .19, .38, .51, .76, .75, 114, 105, 136, 162, 190, 209, 264,

10 : A164010: .23, .46, .57, .92, .85, 138, 119, 152, 171, 200, 220, 276,

11 : A164011: .29, .58, .69, 116, .95, 174, 133, 184, 189, 230, 231, 348,

12 : A164012: .31, .62, .87, 124, 115, 186, 147, 232, 207, 250, 242, 372,

...

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 (mathar(AT)strw.leidenuniv.nl), Aug 09 2009]

Cf. A000027, A000040, A033676, A147861, A163100, A164000.

Cf. Columns: 1=A008578, 2=A161344, 3=A161345, 4=A161424, 5=A161835, 6=A162526, 7=A162527, 8=A162528, 9=A162529, 10=A162530, 11=A162531, 12=A162532.

Cf. Rows: 1=A000290, 2=A002378, 4=A164004, 6=A164006, 7=A164007, 8=A164008, 9=A164009, 10=A164010, 11=A164011, 12=A164012.

Cf. A163990. [From Omar E. Pol (info(AT)polprimos.com), Oct 24 2009]

Sequence in context: A143516 A120620 A094608 this_sequence A056537 A083221 A075652

Adjacent sequences: A163277 A163278 A163279 this_sequence A163281 A163282 A163283

nonn,tabl

Omar E. Pol (info(AT)polprimos.com), Aug 07 2009

Edited by Omar E. Pol (info(AT)polprimos.com), Aug 08 2009