

A080504


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


6



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, 25015118625000, 1, 2, 3, 4, 5, 6, 11, 17757684573750000, 1, 2, 3, 4, 5, 6, 7, 8, 19699405917187500, 1, 2, 3, 4, 5, 6, 7, 8, 14, 295491088757812500, 1, 2, 3, 4, 5, 6, 7
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OFFSET

1,3


COMMENTS

Row n has the form {1,2,...,n2,x,y} where n1 <= x < y. x is minimal such that y exists.


LINKS

Table of n, a(n) for n=1..62.


EXAMPLE

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.


CROSSREFS

Cf. A080505, A081556, A080506, A080507, A080508, A080511.
Sequence in context: A199378 A318522 A005482 * A327958 A154490 A051995
Adjacent sequences: A080501 A080502 A080503 * A080505 A080506 A080507


KEYWORD

nonn,tabl


AUTHOR

Amarnath Murthy, Mar 20 2003


STATUS

approved



