

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
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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



