%I A094270
%S A094270 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 A094270 1173,1174,1175,1176,687371,687372,687373,687374,687375,687376,687377,
%U A094270 687378,236241851618,236241851619,236241851620,236241851621
%N A094270 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 A094270 Martin Fuller, <a href="b094270.txt">Table of n, a(n) for n = 1..78</
               a>
%F A094270 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 (mathar(AT)strw.leidenuniv.nl), 
               Jun 23 2006
%e A094270 Triangle begins:
%e A094270 1
%e A094270 2 3
%e A094270 4 5 6
%e A094270 7 8 9 10
%e A094270 12 13 14 15 16
%e A094270 47 48 49 50 51 52
%e A094270 Product of the terms of the 4-th row = 7*8*9*10 = 5040. Product of the 
               terms of the 5-th row = 12*13*14*15*16 = 524160 = 104*5040.
%p A094270 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 (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
%Y A094270 Cf. A094271, A094272, A094273, A094274.
%Y A094270 Sequence in context: A004744 A072226 A074402 this_sequence A125705 A154314 
               A005524
%Y A094270 Adjacent sequences: A094267 A094268 A094269 this_sequence A094271 A094272 
               A094273
%K A094270 tabl,nonn
%O A094270 1,2
%A A094270 Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 27 2004
%E A094270 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 23 2006
%E A094270 Further terms from Martin Fuller (martin_n_fuller(AT)btinternet.com), 
               Jun 13 2007
%E A094270 Edited by N. J. A. Sloane (njas(AT)research.att.com), Jun 13 2007