A322794 - OEIS

%I #16 Jul 14 2019 06:30:41

%S 1,1,1,2,1,2,1,2,2,2,1,2,1,2,2,3,1,2,1,2,2,2,1,3,2,2,2,2,1,2,1,2,2,2,

%T 2,4,1,2,2,3,1,2,1,2,2,2,1,2,2,2,2,2,1,3,2,3,2,2,1,4,1,2,2,4,2,2,1,2,

%U 2,2,1,2,1,2,2,2,2,2,1,2,3,2,1,4,2,2,2

%N Number of factorizations of n into factors > 1 where all factors have the same number of prime factors counted with multiplicity.

%C Also the number of uniform multiset partitions of the multiset of prime indices of n, where a multiset partition is uniform if all parts have the same size.

%H Gus Wiseman, <a href="/A038041/a038041.txt">Sequences counting and ranking multiset partitions whose part lengths, sums, or averages are constant or strict.</a>

%e The a(1260) = 13 factorizations:

%e   (1260)  (18*70)   (4*9*35)   (2*2*3*3*5*7)

%e           (20*63)   (6*6*35)

%e           (28*45)   (4*15*21)

%e           (30*42)   (6*10*21)

%e           (12*105)  (6*14*15)

%e                     (9*10*14)

%e The a(1260) = 13 multiset partitions:

%e   {{1},{1},{2},{2},{3},{4}}

%e      {{1,1},{2,2},{3,4}}

%e      {{1,1},{2,3},{2,4}}

%e      {{1,2},{1,2},{3,4}}

%e      {{1,2},{1,3},{2,4}}

%e      {{1,2},{1,4},{2,3}}

%e      {{2,2},{1,3},{1,4}}

%e       {{1,1,2},{2,3,4}}

%e       {{1,2,2},{1,3,4}}

%e       {{1,1,3},{2,2,4}}

%e       {{1,1,4},{2,2,3}}

%e       {{1,2,3},{1,2,4}}

%e        {{1,1,2,2,3,4}}

%t facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];

%t Table[Length[Select[facs[n],SameQ@@PrimeOmega/@#&]],{n,100}]

%Y Cf. A001055, A001222, A038041, A112798, A306017, A306021, A319169, A320324, A317583, A321455, A321469, A326514, A326515, A326516.

%K nonn

%O 1,4

%A _Gus Wiseman_, Dec 26 2018