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

%I A056472 #16 Mar 17 2015 02:12:31
%S A056472 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 A056472 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 A056472 2,10,2,2,5,4,5,21,3,7,22,2,11,23,24,2,12,2,2
%N A056472 Triangle read by rows in which row n lists all factorizations of n.
%C A056472 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 A056472 E.g., 12 = 2*6 = 2*2*3 = 3*4
%e A056472 1;
%e A056472 2;
%e A056472 3;
%e A056472 4,2,2;
%e A056472 5;
%e A056472 6,2,3;
%e A056472 7;
%e A056472 8,2,4,2,2,2;
%e A056472 9,3,3;
%e A056472 10,2,5;
%e A056472 11;
%e A056472 12,2,6,2,2,3,3,4;
%o A056472 (Sage)
%o A056472 def factorizations(n) : return fact_helper(n, 2)
%o A056472 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 A056472 # _Eric M. Schmidt_, Jun 06 2014
%Y A056472 Cf. A076709, A162247.
%K A056472 nonn,tabf
%O A056472 1,2
%A A056472 _Donald S. McDonald_, Dec 07 2002
%E A056472 More terms from _Eric M. Schmidt_, Jun 06 2014