cp's OEIS Frontend

A296118 Number of ways to choose a factorization of each factor in a strict factorization of n.

%I A296118 #13 Oct 08 2018 08:08:24
%S A296118 1,1,1,2,1,3,1,5,2,3,1,8,1,3,3,8,1,8,1,8,3,3,1,20,2,3,5,8,1,12,1,18,3,
%T A296118 3,3,23,1,3,3,20,1,12,1,8,8,3,1,45,2,8,3,8,1,20,3,20,3,3,1,38,1,3,8,
%U A296118 34,3,12,1,8,3,12,1,66,1,3,8,8,3,12,1,45,8,3
%N A296118 Number of ways to choose a factorization of each factor in a strict factorization of n.
%H A296118 Antti Karttunen, <a href="/A296118/b296118.txt">Table of n, a(n) for n = 1..16384</a>
%H A296118 Antti Karttunen, <a href="/A296118/a296118.txt">Data supplement: n, a(n) computed for n = 1..100000</a>
%F A296118 Dirichlet g.f.: Product_{n > 1}(1 + A001055(n)/n^s).
%e A296118 The a(12) = 8 twice-factorizations are (2)*(2*3), (2)*(6), (3)*(2*2), (3)*(4), (2*2*3), (2*6), (3*4), (12).
%t A296118 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A296118 Table[Sum[Times@@(Length[facs[#]]&/@f),{f,Select[facs[n],UnsameQ@@#&]}],{n,100}]
%o A296118 (PARI)
%o A296118 A001055(n, m=n) = if(1==n, 1, sumdiv(n, d, if((d>1)&&(d<=m), A001055(n/d, d))));
%o A296118 A296118(n, m=n) = ((n<=m)*A001055(n) + sumdiv(n, d, if((d>1)&&(d<=m)&&(d<n), A001055(d)*A296118(n/d, d-1)))); \\ _Antti Karttunen_, Oct 08 2018
%Y A296118 Cf. A000009, A005117, A045778, A261049, A271619, A281113, A294788, A295923, A296119, A296121.
%K A296118 nonn
%O A296118 1,4
%A A296118 _Gus Wiseman_, Dec 05 2017