cp's OEIS Frontend

A319269 Number of uniform factorizations of n into factors > 1, where a factorization is uniform if all factors appear with the same multiplicity.

%I A319269 #5 Sep 16 2018 21:36:32
%S A319269 1,1,1,2,1,2,1,3,2,2,1,3,1,2,2,4,1,3,1,3,2,2,1,5,2,2,3,3,1,5,1,4,2,2,
%T A319269 2,7,1,2,2,5,1,5,1,3,3,2,1,7,2,3,2,3,1,5,2,5,2,2,1,9,1,2,3,8,2,5,1,3,
%U A319269 2,5,1,9,1,2,3,3,2,5,1,7,4,2,1,9,2,2,2
%N A319269 Number of uniform factorizations of n into factors > 1, where a factorization is uniform if all factors appear with the same multiplicity.
%F A319269 a(n) = Sum_{d|A052409(n)} A045778(n^(1/d)).
%e A319269 The a(144) = 17 factorizations:
%e A319269   (144),
%e A319269   (2*72), (3*48), (4*36), (6*24), (8*18), (9*16), (12*12),
%e A319269   (2*3*24), (2*4*18), (2*6*12), (2*8*9), (3*4*12), (3*6*8),
%e A319269   (2*2*6*6), (2*3*4*6), (3*3*4*4).
%t A319269 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A319269 Table[Length[Select[facs[n],SameQ@@Length/@Split[#]&]],{n,100}]
%Y A319269 Cf. A001055, A045778, A047966, A052409, A072774, A296132, A303386, A317710, A317712, A317717, A317718.
%K A319269 nonn
%O A319269 1,4
%A A319269 _Gus Wiseman_, Sep 16 2018