cp's OEIS Frontend

A296121 Number of twice-factorizations of n with no repeated factorizations.

%I A296121 #21 Sep 20 2018 00:31:25
%S A296121 1,1,1,2,1,3,1,5,2,3,1,8,1,3,3,10,1,8,1,8,3,3,1,20,2,3,5,8,1,12,1,20,
%T A296121 3,3,3,25,1,3,3,20,1,12,1,8,8,3,1,47,2,8,3,8,1,20,3,20,3,3,1,38,1,3,8,
%U A296121 40,3,12,1,8,3,12,1,68,1,3,8,8,3,12,1,47,10
%N A296121 Number of twice-factorizations of n with no repeated factorizations.
%C A296121 From _Robert G. Wilson v_, Dec 05 2017: (Start)
%C A296121 a(n) = 1 iff n equals 1 or is a prime;
%C A296121 a(n) = 2 iff n is a prime squared;
%C A296121 a(n) = 3 iff n is a squarefree semiprime;
%C A296121 a(n) = 5 iff n is a prime cube;
%C A296121 a(n) = 8 iff n is of the form p^2*q, etc.
%C A296121 (End)
%H A296121 Robert G. Wilson v, <a href="/A296121/b296121.txt">Table of n, a(n) for n = 1..1000</a>
%e A296121 The a(12) = 8 twice-factorizations:
%e A296121 (2)*(2*3), (3)*(2*2), (2*2*3),
%e A296121 (2)*(6), (2*6),
%e A296121 (3)*(4), (3*4),
%e A296121 (12).
%t A296121 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A296121 Table[Length[Join@@Table[Select[Tuples[facs/@p],UnsameQ@@#&],{p,facs[n]}]],{n,100}]
%Y A296121 Cf. A001055, A045778, A050345, A063834, A089723, A281113, A296118, A296119, A296120, A296122.
%K A296121 nonn
%O A296121 1,4
%A A296121 _Gus Wiseman_, Dec 05 2017