A077553 Triangle in which the n-th row contains n distinct composite numbers with the least product and has least number of prime divisors. No member of a row is a multiple of another member of the row.

4, 4, 6, 4, 6, 9, 4, 6, 9, 10, 4, 6, 9, 10, 15, 4, 6, 9, 10, 15, 25, 4, 6, 9, 10, 14, 15, 21, 4, 6, 9, 10, 14, 15, 21, 25, 4, 6, 9, 10, 14, 15, 21, 25, 35, 4, 6, 9, 10, 14, 15, 21, 25, 35, 49, 4, 6, 9, 10, 14, 15, 21, 22, 25, 33, 35, 4, 6, 9, 10, 14, 15, 21, 22, 25, 33, 35, 49, 4, 6, 9, 10

Offset: 1

Author

Amarnath Murthy, Nov 10 2002

Keywords

• nonn
• tabl

Comments

If there are two sets of distinct composite numbers satisfying the above condition then the set with lesser product is chosen irrespective of the number of prime divisors. Perhaps the ambiguity may not arise. E.g., row 6 is 4,6,9,10,15,25. This row cannot be extended to get the next row without bringing in another prime because every number divisible by 2,3 or 5 will be a multiple of one of the previous terms. Hence in row 7, prime 7 has to be brought in and then we get a new set of numbers: 4,6,9,10,14,15,21.

Examples

			4;
4,6;
4,6,9;
4,6,9,10;
4,6,9,10,15;
4,6,9,10,15,25;
4,6,9,10,14,15,21;
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..5050 (rows 1..100 flattened)

Crossrefs

Cf. A001358, A005843, A077554, A077555, A087112.

Extensions

More terms from Ray Chandler, Aug 21 2003

Offset corrected by Sean A. Irvine, May 28 2025