A251637 Square array read by antidiagonals containing in row n the multiples of prime(n) in A098550 in order of appearance.

2, 3, 4, 15, 9, 8, 14, 5, 15, 14, 22, 35, 25, 6, 6, 39, 11, 7, 35, 12, 12, 51, 13, 33, 21, 10, 21, 16, 38, 17, 26, 55, 28, 20, 27, 10, 69, 19, 85, 65, 44, 91, 45, 39, 20, 87, 23, 95, 34, 91, 99, 49, 85, 33, 22, 62, 29, 115, 57, 68, 52, 77, 63, 55, 45, 26, 74

Offset: 1

Author

Reinhard Zumkeller, Dec 07 2014

Keywords

• nonn
• tabl

Comments

T(n,k) = A251715(n,k)*A000040(n); A251715(n,k) = T(n,k)/A000040(n);

T(n,k) = A098550(A251716(n,k)); A251716(n,k) = A098551(T(n,k));

T(n,1) = A251618(n); for n > 4: T(n,2) = A000040(n);

conjecture: A098550 is a permutation of the positive integers iff A001221(n) = number of rows containing n.

A251541 = first column, and A251544 = third column for row numbers > 4. - Reinhard Zumkeller, Dec 16 2014

Examples

			.   n   p |  first 14 multiples of p = prime(n) in A098550, n = 1..25
.  -------+-------------------------------------------------------------
.   1   2 |   2  4   8  14   6  12  16  10   20  22   26   28   32   18
.   2   3 |   3  9  15   6  12  21  27  39   33  45   51   18   24   36
.   3   5 |  15  5  25  35  10  20  45  85   55  65   30   95   40   50
.   4   7 |  14 35   7  21  28  91  49  63   42  56   77  119  133  161
.   5  11 |  22 11  33  55  44  99  77  66   88 165  143  121  187  110
.   6  13 |  39 13  26  65  91  52 117  78  104 195  143  130  156  221
.   7  17 |  51 17  85  34  68 119 153 102  187 136  170  255  221  204
.   8  19 |  38 19  95  57 133  76 171 114  152 209  247  190  285  228
.   9  23 |  69 23 115  46 161  92 138 207  184 253  299  345  230  276
.  10  29 |  87 29  58 145 203 116 174 261  232 319  377  290  435  348
.  11  31 |  62 31  93 155 124 217 279 186  341 403  248  465  310  372
.  12  37 |  74 37 111 185 148 259 222 333  296 407  555  370  629  481
.  13  41 | 123 41  82 205 164 287 246 369  451 328  410  533  615  492
.  14  43 |  86 43 129 215 172 301 387 258  473 344  430  645  559  516
.  15  47 |  94 47 329 141 235 188 282 423  517 376  470  611  705  564
.  16  53 | 106 53 265 159 212 371 318 477  424 583  689  530  795  636
.  17  59 | 118 59 177 295 236 413 354 531  649 472  767  590  885 1003
.  18  61 | 122 61 427 183 305 244 366 549  671 488  793  610  915  732
.  19  67 | 201 67 335 134 268 469 603 402  536 737  871  670 1005  804
.  20  71 | 142 71 213 355 284 497 426 639  568 781  710 1065  923  852
.  21  73 | 146 73 365 219 292 511 438 657  584 803  730  949 1095  876
.  22  79 | 158 79 237 395 316 553 474 711  632 869 1027  790 1185  948
.  23  83 | 249 83 581 166 415 332 498 747  913 664 1079  830 1245  996
.  24  89 | 178 89 267 445 356 623 534 801  712 979 1157  890 1335 1068
.  25  97 | 291 97 679 194 485 388 582 873 1067 776  970 1261 1455 1164 .
.  ---------------------------------------------------------------------
See also A251715 for a table with T(n,k)/p and A251716 for a table of indices of T(n,k) within A098550.
		

Links

• Reinhard Zumkeller, Rows n = 1..125 of triangle, flattened

Crossrefs

Cf. A098550, A000040, A251618 (first column), A001221, A251715, A251716.

Cf. A251541, A251544.

Programs

Haskell

when seen as table read by rows:
a251637 n k = a251637_tabl !! (n-1) !! (k-1)
a251637_row n= a251637_tabl !! (n-1)
a251637_tabl = adias $ map
   (\k -> filter
     ((== 0) . flip mod (fromInteger $ a000040 k)) a098550_list) [1..]

Mathematica

rows = 25; (* f = A098550 *) Clear[f, row]; f[n_ /; n <= 3] := n; f[n_] := f[n] = Module[{k}, For[k=4, GCD[f[n-2], k] == 1 || GCD[f[n-1], k]>1 || MemberQ[Array[f, n-1], k], k++]; k]; row[n_] := row[n] = Module[{k, cnt}, Reap[For[k=1; cnt=0, cnt <= rows-n, k++, If[Divisible[f[k], Prime[n]], cnt++; Sow[f[k]]]]][[2, 1]]]; A251637 = Table[row[n-k+1][[k]], {n, 1, rows}, {k, 1, n}] // Flatten (* Jean-François Alcover, Dec 17 2014 *)