A257836 Numbers which are the product of at least two consecutive odd numbers > 1.

15, 35, 63, 99, 105, 143, 195, 255, 315, 323, 399, 483, 575, 675, 693, 783, 899, 945, 1023, 1155, 1287, 1295, 1443, 1599, 1763, 1935, 2115, 2145, 2303, 2499, 2703, 2915, 3135, 3315, 3363, 3465, 3599, 3843, 4095, 4355, 4623, 4845, 4899, 5183, 5475, 5775, 6083

Offset: 1

Author

Reinhard Zumkeller, May 12 2015

Keywords

• nonn

Examples

			.     |       |   ----- Factorizations into ... --------------
.   n |  a(n) |   prime powers     |   consecutive odd numbers
. ----+-------+--------------------+--------------------------
.   1 |    15 |   3 * 5            |   3 * 5
.   2 |    35 |   5 * 7            |   5 * 7
.   3 |    63 |   3^2 * 7          |   7 * 9
.   4 |    99 |   3^2 * 11         |   9 * 11
.   5 |   105 |   3 * 5 * 7        |   3 * 5 * 7
.   6 |   143 |   11 * 13          |   11 * 13
.   7 |   195 |   3 * 5 * 13       |   13 * 15
.   8 |   255 |   3 * 5 * 17       |   15 * 17
.   9 |   315 |   3^2 * 5 * 7      |   5 * 7 * 9
.  10 |   323 |   17 * 19          |   17 * 19
.  11 |   399 |   3 * 7 * 19       |   19 * 21
.  12 |   483 |   3 * 7 * 23       |   21 * 23
.  13 |   575 |   5^2 * 23         |   23 * 25
.  14 |   675 |   3^3 * 5^2        |   25 * 27
.  15 |   693 |   3^2 * 7 * 11     |   7 * 9 * 11
.  16 |   783 |   3^3 * 29         |   27 * 29
.  17 |   899 |   29 * 31          |   29 * 31
.  18 |   945 |   3^3 * 5 * 7      |   3 * 5 * 7 * 9
.  19 |  1023 |   3 * 11 * 31      |   31 * 33
.  20 |  1155 |   3 * 5 * 7 * 11   |   33 * 35
.  21 |  1287 |   3^2 * 11 * 13    |   9 * 11 * 13
.  22 |  1295 |   5 * 7 * 37       |   35 * 37
.  23 |  1443 |   3 * 13 * 37      |   37 * 39
.  24 |  1599 |   3 * 13 * 41      |   39 * 41
.  25 |  1763 |   41 * 43          |   41 * 43
.  26 |  1935 |   3^2 * 5 * 43     |   43 * 45
.  27 |  2115 |   3^2 * 5 * 47     |   45 * 47
.  28 |  2145 |   3 * 5 * 11 * 13  |   11 * 13 * 15
.  29 |  2303 |   7^2 * 47         |   47 * 49
.  30 |  2499 |   3 * 7^2 * 17     |   49 * 51  .
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005408, A097889.

Programs

Haskell

import Data.Set (singleton, deleteFindMin, insert)
a257836 n = a257836_list !! (n-1)
a257836_list = f $ singleton (15, 3, 5) where
   f s = y : f (insert (w, u, v') $ insert (w `div` u, u + 2, v') s')
         where w = y * v'; v' = v + 2
               ((y, u, v), s') = deleteFindMin s