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Triangle read by rows: row n contains the least set of n successive numbers whose product is a multiple of the product of the previous row. The first term of each row must be larger than the last term of the previous row.
5

%I #14 Mar 13 2015 19:09:26

%S 1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,47,48,49,50,51,52,1170,1171,1172,

%T 1173,1174,1175,1176,687371,687372,687373,687374,687375,687376,687377,

%U 687378,236241851618,236241851619,236241851620,236241851621

%N Triangle read by rows: row n contains the least set of n successive numbers whose product is a multiple of the product of the previous row. The first term of each row must be larger than the last term of the previous row.

%H Martin Fuller, <a href="/A094270/b094270.txt">Table of n, a(n) for n = 1..78</a>

%F product{k=1,..,n} a(n,k) | product{k=1,..,n+1} a(n+1,k). a(n,k+1)=a(n,k)+1 for k=1,..,n-1. a(n,1)>a(n-1,n-1). - _R. J. Mathar_, Jun 23 2006

%e Triangle begins:

%e 1

%e 2 3

%e 4 5 6

%e 7 8 9 10

%e 12 13 14 15 16

%e 47 48 49 50 51 52

%e Product of the terms of the 4th row = 7*8*9*10 = 5040. Product of the terms of the 5th row = 12*13*14*15*16 = 524160 = 104*5040.

%p A094270 := proc(nmax) local a,k,strt,aproo,apro,i,j,s; a := array(1..nmax,1..nmax); a[1,1] := 1; print(a[1,1]); k := 2; while k < nmax do strt := a[k-1,k-1]+1; aproo := product(a[k-1,i],i=1..k-1); while true do apro := product(strt+j-1,j=1..k); if ( apro mod aproo ) =0 then for s from 1 to k do a[k,s] := strt+s-1; print(a[k,s]); od; break; fi; strt := strt+1; od; k := k+1; od; RETURN(a); end: A094270(10) : # _R. J. Mathar_, Jun 23 2006

%Y Cf. A094271, A094272, A094273, A094274.

%K tabl,nonn

%O 1,2

%A _Amarnath Murthy_, Apr 27 2004

%E More terms from _R. J. Mathar_, Jun 23 2006

%E Further terms from _Martin Fuller_, Jun 13 2007

%E Edited by _N. J. A. Sloane_, Jun 13 2007