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A080504 Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose arithmetic and geometric means are both integers. 6

%I

%S 1,1,9,1,2,108,1,2,5,1000,1,2,3,4,1012500,1,2,3,4,8,15552,1,2,3,4,5,6,

%T 25015118625000,1,2,3,4,5,6,11,17757684573750000,1,2,3,4,5,6,7,8,

%U 19699405917187500,1,2,3,4,5,6,7,8,14,295491088757812500,1,2,3,4,5,6,7

%N Triangle whose n-th row contains the least set (ordered lexicographically) of n distinct positive integers whose arithmetic and geometric means are both integers.

%C Row n has the form {1,2,...,n-2,x,y} where n-1 <= x < y. x is minimal such that y exists.

%e The fourth row contains 1,2,5,1000, with AM=252 and GM=10. There is no set of the form {1,2,3,y} or {1,2,4,y} whose AM and GM are both integers.

%Y Cf. A080505, A081556, A080506, A080507, A080508, A080511.

%K nonn,tabl

%O 1,3

%A _Amarnath Murthy_, Mar 20 2003

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Last modified July 15 16:09 EDT 2019. Contains 325049 sequences. (Running on oeis4.)