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

1,2

Comments

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

Links

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

Sean A. Irvine, Java program (github)

Example

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

Crossrefs

Cf. A076027, A076028, A076029, A076030.

Cf. A076596, A076696.

Sequence in context: A385569 A321984 A083486 * A076596 A081967 A076099

Adjacent sequences: A076028 A076029 A076030 * A076032 A076033 A076034

Keyword

nonn,tabl

Author

Amarnath Murthy, Oct 01 2002

Extensions

Corrected and extended by Hans Havermann, Nov 09 2002

Status

approved