A056472 Triangle read by rows in which row n lists all factorizations of n.

1, 2, 3, 4, 2, 2, 5, 6, 2, 3, 7, 8, 2, 4, 2, 2, 2, 9, 3, 3, 10, 2, 5, 11, 12, 2, 6, 2, 2, 3, 3, 4, 13, 14, 2, 7, 15, 3, 5, 16, 2, 8, 2, 2, 4, 2, 2, 2, 2, 4, 4, 17, 18, 2, 9, 2, 3, 3, 3, 6, 19, 20, 2, 10, 2, 2, 5, 4, 5, 21, 3, 7, 22, 2, 11, 23, 24, 2, 12, 2, 2

Offset: 1

Author

Donald S. McDonald, Dec 07 2002

Keywords

• nonn
• tabf

Comments

n comes first, then minimal factorization (12=2*6). Resultant factor is further resolved as much as possible, (2*6 = 2*2*3). The natural number or initial factors are then incremented, (3*4, 13.)

Examples

			E.g., 12 = 2*6 = 2*2*3 = 3*4
1;
2;
3;
4,2,2;
5;
6,2,3;
7;
8,2,4,2,2,2;
9,3,3;
10,2,5;
11;
12,2,6,2,2,3,3,4;
		

Crossrefs

Cf. A076709, A162247.

Programs

Sage

def factorizations(n) : return fact_helper(n, 2)
def fact_helper(n, min) : return sum(([[d] + F for F in fact_helper(n//d, d)] for d in divisors(n) if d >= min and d <= isqrt(n)), [[n]])
# Eric M. Schmidt, Jun 06 2014

Extensions

More terms from Eric M. Schmidt, Jun 06 2014