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

1,1

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.

Links

Table of n, a(n) for n=1..64.

Example

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.

Sequence in context: A255129 A119586 A095904 * A083140 A246279 A285112

Adjacent sequences: A096150 A096151 A096152 * A096154 A096155 A096156

Keyword

nonn,tabl

Author

Alford Arnold, Jul 24 2004

Extensions

Edited by Peter Munn, Oct 23 2023

Status

approved