A080507 -id:A080507 - cp's OEIS frontend

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

Amarnath Murthy, Mar 20 2003

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

			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.

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

A081556 Next-to-last term in n-th row of A080504.

Original entry on oeis.org

1, 2, 5, 4, 8, 6, 11, 8, 14, 10, 17, 12, 20, 14, 23, 16, 26, 18, 29, 20, 32, 22, 32, 24, 38, 26, 41, 28, 44, 30, 47, 32, 50, 34, 53, 36, 56, 38, 59, 40, 62, 42, 65, 44, 68, 46, 71, 48, 74, 50, 77, 52, 80, 54, 83, 56, 86, 58, 89, 60, 92, 62, 95, 64, 98, 66, 101, 68, 104, 70

Offset: 2

Dean Hickerson, Mar 21 2003

nonn

If n is odd, a(n) = n-1. If n is even, n-1 <= a(n) <= 3n/2-1. For even n up to 100, a(n) = 3n/2-1 unless n = 2 or 24; are there other exceptions? - Dean Hickerson, Mar 21 2003

			a(24)=32 since the 24th row of A080504 can be exhibited as: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 32, y with y = 3^15*5^20*7^21*11^22*13^23*17^23*19^23.

Cf. A080504, A080505, A080506, A080507.

A080505 Last term in n-th row of A080504.

Original entry on oeis.org

1, 9, 108, 1000, 1012500, 15552, 25015118625000, 17757684573750000, 19699405917187500, 295491088757812500, 2754030502015722328328015625000, 69471494082638078965978431093750000

Offset: 1

Amarnath Murthy, Mar 20 2003

nonn

Cf. A080504, A081556, A080506, A080507.

A080506 Geometric mean of n-th row of A080504.

Original entry on oeis.org

1, 3, 6, 10, 30, 12, 210, 330, 210, 210, 2310, 3570, 30030, 2310, 30030, 690690, 510510, 30030, 9699690, 14804790, 9699690, 19399380, 223092870, 9699690, 223092870, 223092870, 223092870, 9146807670, 6469693230, 223092870

Offset: 1

Amarnath Murthy, Mar 20 2003

nonn

Cf. A080504, A080505, A081556, A080507.

cp's OEIS Frontend

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.

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A081556 Next-to-last term in n-th row of A080504.

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A080505 Last term in n-th row of A080504.

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A080506 Geometric mean of n-th row of A080504.

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