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%I #5 Aug 02 2022 15:40:53
%S 5,11,25,55,125,277,637,1421,3237,7553,16807,38661,90209,208397
%N a(n) is the largest integer value of Product_{k=1..n} (2 + 1/t_k) with integers t_k > 1.
%e a(2) = 5 = (2 + 1/3) * (2 + 1/7),
%e a(3) = 11 = (2 + 1/3) * (2 + 1/5) * (2+1/7) = (2 + 1/3)^2 * (2 + 1/49),
%e a(7) = 277 = (2 + 1/3)^5 * ( 2 + 1/405) * (2 + 1/13630477).
%o (PARI) see link in A355626
%Y A355626 gives more information.
%Y A355630 same problem with factors (3 + 1/t_k).
%K nonn,hard,more
%O 2,1
%A _Hugo Pfoertner_ and _Markus Sigg_, Jul 16 2022