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A056472 Triangle read by rows in which row n lists all factorizations of n. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 15 20:04 EDT 2019. Contains 328037 sequences. (Running on oeis4.)