A076031 -id:A076031 - cp's OEIS frontend

A077168 Lexicographically earliest infinite sequence of distinct positive numbers with the property that when written as a triangle, the product of each row is a factorial.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 259200, 15, 16, 17, 18, 19, 87178291200, 20, 21, 22, 23, 24, 25, 202741834014720, 26, 27, 28, 29, 30, 31, 32, 484725313854093312000000, 33, 34, 35, 36, 37, 38, 39, 40, 4438779300500903005519872000000, 41, 42, 43, 44

Offset: 0

Amarnath Murthy, Nov 01 2002

The old definition was "Triangle formed by grouping the natural numbers so that the n-th group contains n numbers whose product is a factorial.". - N. J. A. Sloane, Oct 06 2024

			Triangle begins:
1,
2, 3,
4, 5, 6,
7, 8, 9, 10,
11, 12, 13, 14, 259200,
15, 16, 17, 18, 19, 87178291200,
20, 21, 22, 23, 24, 25, 202741834014720,
26, 27, 28, 29, 30, 31, 32, 484725313854093312000000,
33, 34, 35, 36, 37, 38, 39, 40, 4438779300500903005519872000000,
...
The row products are:
 1 = 1!
 2*3 = 6 = 3!
 4*5*6 = 120 = 5!
 7*8*9*10 = 5040 = 7!
 11*12*13*14*259200 = 6227020800 = 13!
 15*16*17*18*19*87178291200 = 121645100408832000 = 19!
 20*21*22*23*24*25*202741834014720 = 25852016738884976640000 = 23!
 26*27*28*29*30*31*32*484725313854093312000000 = 8222838654177922817725562880000000 = 31!
 33*34*35*36*37*38*39*40*4438779300500903005519872000000 = 37!
 ...

Cf. A076031, A077169, A077170, A077171.

More terms from Sascha Kurz, Feb 10 2003

Entry revised by N. J. A. Sloane, Oct 06 2024

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

A077168 Lexicographically earliest infinite sequence of distinct positive numbers with the property that when written as a triangle, the product of each row is a factorial.

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