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

1,2

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.)

Links

Table of n, a(n) for n=1..81.

Example

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;

Prog

(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

Crossrefs

Cf. A076709, A162247.

Sequence in context: A182710 A182711 A138136 * A162247 A264809 A035578

Adjacent sequences: A056469 A056470 A056471 * A056473 A056474 A056475

Keyword

nonn,tabf

Author

Donald S. McDonald, Dec 07 2002

Extensions

More terms from Eric M. Schmidt, Jun 06 2014

Status

approved