A056472 - OEIS

%I #16 Mar 17 2015 02:12:31

%S 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,

%T 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,

%U 2,10,2,2,5,4,5,21,3,7,22,2,11,23,24,2,12,2,2

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

%C 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.)

%e E.g., 12 = 2*6 = 2*2*3 = 3*4

%e 1;

%e 2;

%e 3;

%e 4,2,2;

%e 5;

%e 6,2,3;

%e 7;

%e 8,2,4,2,2,2;

%e 9,3,3;

%e 10,2,5;

%e 11;

%e 12,2,6,2,2,3,3,4;

%o (Sage)

%o def factorizations(n) : return fact_helper(n, 2)

%o 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]])

%o # _Eric M. Schmidt_, Jun 06 2014

%Y Cf. A076709, A162247.

%K nonn,tabf

%O 1,2

%A _Donald S. McDonald_, Dec 07 2002

%E More terms from _Eric M. Schmidt_, Jun 06 2014