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

%I A248164 #9 Oct 05 2014 09:33:27
%S A248164 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 A248164 77,30,105,385,210,1155,2310,2,3,5,7,11,13,6,15,35,77,143,30,105,385,
%U A248164 1001,210,1155,5005,2310,15015,30030,2,3,5,7,11,13,17,6,15
%N A248164 Table read by rows: n-th row contains the products of all consecutive subsets of the first n primes in their natural order.
%C A248164 T(n,A000217(n)) = A002110(n).
%H A248164 Reinhard Zumkeller, <a href="/A248164/b248164.txt">Rows n = 1..25 of triangle, flattened</a>
%e A248164 .  1:  2
%e A248164 .  2:  2,3,6
%e A248164 .  3:  2,3,5,6,15,30
%e A248164 .  4:  2,3,5,7,6,15,35,30,105,210
%e A248164 .  5:  2,3,5,7,11,6,15,35,77,30,105,385,210,1155,2310
%e A248164 .  6:  2,3,5,7,11,13,6,15,35,77,143,30,105,385,1001,210,1155,5005,2310,15015,30030
%e A248164 The prime factors of these terms form consecutive primes, see also A248147.
%e A248164 .  1: [2]
%e A248164 .  2: [2] [3] [2,3]
%e A248164 .  3: [2] [3] [5] [2,3] [3,5] [2,3,5]
%e A248164 .  4: [2] [3] [5] [7] [2,3] [3,5] [5,7] [2,3,5] [3,5,7] [2,3,5,7]
%e A248164 .  5: [2] [3] [5] [7] [11] [2,3] [3,5] [5,7] [7,11] [2,3,5] [3,5,7] ...
%e A248164 .  6: [2] [3] [5] [7] [11] [13] [2,3] [3,5] [5,7] [7,11] [11,13] [2,3,5] ...
%o A248164 (Haskell)
%o A248164 import Data.List (group)
%o A248164 a248164 n k = a248164_tabf !! (n-1) !! (k-1)
%o A248164 a248164_row n = a248164_tabf !! (n-1)
%o A248164 a248164_tabf = map (map product) psss where
%o A248164    psss = iterate f [[2]] where
%o A248164       f pss = group (h $ last pss) ++ map h pss
%o A248164       h ws = ws ++ [a151800 $ last ws]
%Y A248164 Cf. A000217 (row lengths), A002110, A151800, A248147.
%K A248164 nonn,tabf,look
%O A248164 1,1
%A A248164 _Reinhard Zumkeller_, Oct 02 2014