A248164 Table read by rows: n-th row contains the products of all consecutive subsets of the first n primes in their natural order.

2, 2, 3, 6, 2, 3, 5, 6, 15, 30, 2, 3, 5, 7, 6, 15, 35, 30, 105, 210, 2, 3, 5, 7, 11, 6, 15, 35, 77, 30, 105, 385, 210, 1155, 2310, 2, 3, 5, 7, 11, 13, 6, 15, 35, 77, 143, 30, 105, 385, 1001, 210, 1155, 5005, 2310, 15015, 30030, 2, 3, 5, 7, 11, 13, 17, 6, 15

Offset: 1

Author

Reinhard Zumkeller, Oct 02 2014

Keywords

• nonn
• tabf
• look

Comments

T(n,A000217(n)) = A002110(n).

Examples

			.  1:  2
.  2:  2,3,6
.  3:  2,3,5,6,15,30
.  4:  2,3,5,7,6,15,35,30,105,210
.  5:  2,3,5,7,11,6,15,35,77,30,105,385,210,1155,2310
.  6:  2,3,5,7,11,13,6,15,35,77,143,30,105,385,1001,210,1155,5005,2310,15015,30030
The prime factors of these terms form consecutive primes, see also A248147.
.  1: [2]
.  2: [2] [3] [2,3]
.  3: [2] [3] [5] [2,3] [3,5] [2,3,5]
.  4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]
.  5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...
.  6: [2] [3] [5] [7] [11] [13] [2,3] [3,5] [5,7] [7,11] [11,13] [2,3,5] ...
		

Links

• Reinhard Zumkeller, Rows n = 1..25 of triangle, flattened

Crossrefs

Cf. A000217 (row lengths), A002110, A151800, A248147.

Programs

Haskell

import Data.List (group)
a248164 n k = a248164_tabf !! (n-1) !! (k-1)
a248164_row n = a248164_tabf !! (n-1)
a248164_tabf = map (map product) psss where
   psss = iterate f [[2]] where
      f pss = group (h $ last pss) ++ map h pss
      h ws = ws ++ [a151800 $ last ws]