A076596 -id:A076596 - cp's OEIS frontend

A076031 Group the natural numbers so that the n-th group contains the smallest still-available set of n numbers whose product is a square.

1, 2, 8, 3, 4, 12, 5, 6, 7, 210, 9, 10, 11, 13, 1430, 14, 15, 16, 17, 18, 1785, 19, 20, 21, 22, 23, 24, 168245, 25, 26, 27, 28, 29, 30, 31, 409045, 32, 33, 34, 35, 36, 37, 38, 39, 119629510, 40, 41, 42, 43, 44, 45, 46, 47, 48, 293493662, 49, 50, 51, 52

Offset: 1

Amarnath Murthy, Oct 01 2002

The first n-1 numbers of row n are selected by simply choosing the smallest n-1 numbers which have not yet been used. The remaining number is then chosen to be the smallest possible unused number such that the product of the n numbers is a square. - Sean A. Irvine, Mar 14 2025

			1;
2, 8;
3, 4, 12;
5, 6, 7, 210;
9, 10, 11, 13, 1430;
14, 15, 16, 17, 18, 1785;
...

Sean A. Irvine, Table of n, a(n) for n = 1..1540 (rows 1..20 flattened)
Sean A. Irvine, Java program (github)

Cf. A076027, A076028, A076029, A076030.

Cf. A076596, A076696.

Corrected and extended by Hans Havermann, Nov 09 2002

A076696 Triangle read by rows: n-th row contains n numbers whose product is a square; all numbers in triangle are distinct.

Original entry on oeis.org

1, 2, 8, 3, 7, 21, 4, 5, 6, 30, 9, 10, 12, 15, 18

Offset: 1

Donald S. McDonald, Nov 10 2002

Second solution. Both solutions are smaller than A076031.

			1^2 4^2 21^2 60^2 540^2 = (1)(2 8)(3 7 21)(4 5 6 30)(9 10 12 15 18)

Cf. A076031, A076596.

It is not clear to me how one decides what numbers to place in the n-th row! - N. J. A. Sloane, Nov 30 2002

cp's OEIS Frontend

A076031 Group the natural numbers so that the n-th group contains the smallest still-available set of n numbers whose product is a square.

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