cp's OEIS Frontend

A327658 Number of factorizations of n that are empty or whose factors have a common divisor > 1.

%I A327658 #4 Sep 22 2019 08:06:09
%S A327658 1,1,1,2,1,1,1,3,2,1,1,2,1,1,1,5,1,2,1,2,1,1,1,4,2,1,3,2,1,1,1,7,1,1,
%T A327658 1,4,1,1,1,4,1,1,1,2,2,1,1,7,2,2,1,2,1,4,1,4,1,1,1,3,1,1,2,11,1,1,1,2,
%U A327658 1,1,1,7,1,1,2,2,1,1,1,7,5,1,1,3,1,1,1
%N A327658 Number of factorizations of n that are empty or whose factors have a common divisor > 1.
%C A327658 First differs from A319786 at a(900) = 11, A319786(900) = 12.
%C A327658 A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798. Numbers whose prime indices have a common divisor > 1 are listed in A318978.
%H A327658 Gus Wiseman, <a href="https://docs.google.com/document/d/e/2PACX-1vSX9dPMGJhxB8rOknCGvOs6PiyhupdWNpqLsnphdgU6MEVqFBnWugAXidDhwHeKqZe_YnUqYeGOXsOk/pub">Sequences counting and encoding certain classes of multisets</a>
%e A327658 The a(120) = 7 factorizations:
%e A327658   (120)
%e A327658   (2*60)
%e A327658   (4*30)
%e A327658   (6*20)
%e A327658   (10*12)
%e A327658   (2*2*30)
%e A327658   (2*6*10)
%t A327658 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A327658 Table[Length[Select[facs[n],#=={}||GCD@@#!=1&]],{n,100}]
%Y A327658 See link for additional cross-references.
%Y A327658 Cf. A000005, A056239, A112798, A281116, A289509, A327406.
%K A327658 nonn
%O A327658 1,4
%A A327658 _Gus Wiseman_, Sep 21 2019