A076596 Triangle read by rows: n-th row contains n numbers whose product is a square; all numbers in the triangle are distinct and the square is as small as possible.

1, 2, 8, 3, 4, 12, 5, 7, 10, 14, 6, 9, 15, 18, 20, 11, 13, 16, 22, 25, 26, 17, 19, 21, 27, 28, 34, 38, 23, 24, 30, 33, 35, 42, 44, 46, 29, 31, 32, 36, 40, 45, 49, 58, 62, 37, 39, 41, 48, 50, 52, 56, 63, 74, 82, 43, 47, 51, 54, 55, 60, 64, 66, 68, 86, 94, 53, 57, 65, 69, 70, 72, 76, 78, 81, 84, 92, 106

Offset

1,2

Comments

Differs from A076031 and A076696.

Links

Table of n, a(n) for n=1..78.

Sean A. Irvine, Java program (github)

Example

Triangle begins:
  1 = 1^2,
  2 * 8 = 4^2,
  3 * 4 * 12 = 12^2,
  5 * 7 * 10 * 14 = 70^2,
  6 * 9 * 15 * 18 * 20 = 540^2,
  11 * 13 * 16 * 22 * 25 * 26 = 5720^2,
  17 * 19 * 21 * 27 * 28 * 34 * 38 = 81396^2,
  23 * 24 * 30 * 33 * 35 * 42 * 44 * 46 = 1275120^2, ...

Crossrefs

Cf. A076031, A076696.

Sequence in context: A397293 A083486 A076031 * A081967 A076099 A199072

Adjacent sequences: A076593 A076594 A076595 * A076597 A076598 A076599

Keyword

nonn,tabl

Author

Donald S. McDonald, Nov 10 2002

Extensions

Name clarified and a(16)-a(36) from Sean A. Irvine, Apr 09 2025

More terms from Bert Dobbelaere, Nov 22 2025

Status

approved