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.

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

Offset

1,3

Comments

Row n has the form {1,2,...,n-2,x,y} where n-1 <= 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