A096153 Natural numbers (greater than 1) arranged in rows according to their ordered prime signature. Square array A(n,k) read by descending antidiagonals.

2, 3, 4, 5, 9, 6, 7, 25, 10, 8, 11, 49, 14, 27, 12, 13, 121, 15, 125, 20, 16, 17, 169, 21, 343, 28, 81, 18, 19, 289, 22, 1331, 44, 625, 50, 24, 23, 361, 26, 2197, 45, 2401, 75, 40, 30, 29, 529, 33, 4913, 52, 14641, 98, 56, 42, 32, 31, 841, 34, 6859, 63, 28561, 147, 88, 66

Offset: 1

Author

Alford Arnold, Jul 24 2004

Keywords

• nonn
• tabl

Comments

The first row is A000040 (the prime numbers) and the first column is A055932 (the Quet prime signatures).

If we restrict the terms to those having ordered prime signatures that are not represented in A025487 (the least prime signature sequence), we get A096011.

Examples

			18 = 2^1 * 3^2, so has ordered prime signature (1,2) given by the exponents in the factorization shown. No earlier number has this prime signature, so 18 is placed at the start of the next empty row (row 7). Thus A(7,1) = 18.
		

Crossrefs

For m >= 2, A077462/A335286 essentially give the row/column containing m.

Cf. A071364, A357126.

See the comments for the relationships with A000040, A025487, A055932, A096011.

Extensions

Edited by Peter Munn, Oct 23 2023