cp's OEIS Frontend

A317176 Number of chains of factorizations of n into factors > 1, ordered by refinement, starting with the prime factorization of n and ending with the maximum factorization (n).

%I A317176 #4 Jul 24 2018 21:21:36
%S A317176 1,1,1,1,1,1,1,2,1,1,1,3,1,1,1,6,1,3,1,3,1,1,1,11,1,1,2,3,1,4,1,18,1,
%T A317176 1,1,15,1,1,1,11,1,4,1,3,3,1,1,49,1,3,1,3,1,11,1,11,1,1,1,21,1,1,3,74,
%U A317176 1,4,1,3,1,4,1,78,1,1,3,3,1,4,1,49,6,1,1
%N A317176 Number of chains of factorizations of n into factors > 1, ordered by refinement, starting with the prime factorization of n and ending with the maximum factorization (n).
%C A317176 If x and y are factorizations of the same integer and it is possible to produce x by further factoring the factors of y, flattening, and sorting, then x <= y.
%F A317176 a(prime^n) = A213427(n).
%e A317176 The a(24) = 11 chains:
%e A317176   (2*2*2*3) < (24)
%e A317176   (2*2*2*3) < (2*12)  < (24)
%e A317176   (2*2*2*3) < (3*8)   < (24)
%e A317176   (2*2*2*3) < (4*6)   < (24)
%e A317176   (2*2*2*3) < (2*2*6) < (24)
%e A317176   (2*2*2*3) < (2*3*4) < (24)
%e A317176   (2*2*2*3) < (2*2*6) < (2*12) < (24)
%e A317176   (2*2*2*3) < (2*2*6) < (4*6)  < (24)
%e A317176   (2*2*2*3) < (2*3*4) < (2*12) < (24)
%e A317176   (2*2*2*3) < (2*3*4) < (3*8)  < (24)
%e A317176   (2*2*2*3) < (2*3*4) < (4*6)  < (24)
%Y A317176 Cf. A001055, A002846, A007716, A045778, A162247, A213427, A275024, A281113, A299202, A317144, A317145, A317146.
%K A317176 nonn
%O A317176 1,8
%A A317176 _Gus Wiseman_, Jul 23 2018