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Table read by rows: n-th row contains the products of all consecutive subsets of the first n primes in their natural order.
3

%I #9 Oct 05 2014 09:33:27

%S 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,

%T 77,30,105,385,210,1155,2310,2,3,5,7,11,13,6,15,35,77,143,30,105,385,

%U 1001,210,1155,5005,2310,15015,30030,2,3,5,7,11,13,17,6,15

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

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

%H Reinhard Zumkeller, <a href="/A248164/b248164.txt">Rows n = 1..25 of triangle, flattened</a>

%e . 1: 2

%e . 2: 2,3,6

%e . 3: 2,3,5,6,15,30

%e . 4: 2,3,5,7,6,15,35,30,105,210

%e . 5: 2,3,5,7,11,6,15,35,77,30,105,385,210,1155,2310

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

%e The prime factors of these terms form consecutive primes, see also A248147.

%e . 1: [2]

%e . 2: [2] [3] [2,3]

%e . 3: [2] [3] [5] [2,3] [3,5] [2,3,5]

%e . 4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]

%e . 5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...

%e . 6: [2] [3] [5] [7] [11] [13] [2,3] [3,5] [5,7] [7,11] [11,13] [2,3,5] ...

%o (Haskell)

%o import Data.List (group)

%o a248164 n k = a248164_tabf !! (n-1) !! (k-1)

%o a248164_row n = a248164_tabf !! (n-1)

%o a248164_tabf = map (map product) psss where

%o psss = iterate f [[2]] where

%o f pss = group (h $ last pss) ++ map h pss

%o h ws = ws ++ [a151800 $ last ws]

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

%K nonn,tabf,look

%O 1,1

%A _Reinhard Zumkeller_, Oct 02 2014