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

1,1

Comments

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

Links

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

Example

.  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] ...

Prog

(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]

Crossrefs

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

Sequence in context: A093422 A297890 A083506 * A338993 A210222 A207621

Adjacent sequences: A248161 A248162 A248163 * A248165 A248166 A248167

Keyword

nonn,tabf,look

Author

Reinhard Zumkeller, Oct 02 2014

Status

approved