cp's OEIS Frontend

A387133 Number of ways to choose a sequence of distinct integer partitions, one of each prime factor of n (with multiplicity).

%I A387133 #8 Aug 28 2025 17:24:44
%S A387133 1,2,3,2,7,6,15,0,6,14,56,6,101,30,21,0,297,12,490,14,45,112,1255,0,
%T A387133 42,202,6,30,4565,42,6842,0,168,594,105,12,21637,980,303,0,44583,90,
%U A387133 63261,112,42,2510,124754,0,210,84,891,202,329931,12,392,0,1470,9130
%N A387133 Number of ways to choose a sequence of distinct integer partitions, one of each prime factor of n (with multiplicity).
%e A387133 The prime factors of 9 are (3,3), and the a(9) = 6 choices are:
%e A387133   ((3),(2,1))
%e A387133   ((3),(1,1,1))
%e A387133   ((2,1),(3))
%e A387133   ((2,1),(1,1,1))
%e A387133   ((1,1,1),(3))
%e A387133   ((1,1,1),(2,1))
%t A387133 Table[Length[Select[Tuples[IntegerPartitions/@Flatten[ConstantArray@@@FactorInteger[n]]],UnsameQ@@#&]],{n,30}]
%Y A387133 For prime factors instead of partitions we have A008966, see A355741.
%Y A387133 Twice partitions of this type are counted by A296122.
%Y A387133 For prime indices instead of factors we have A387110, see A387136.
%Y A387133 For strict partitions and prime indices we have A387115.
%Y A387133 For constant partitions and prime indices we have A387120.
%Y A387133 Positions of zero are A387326, for indices apparently A276079 (complement A276078).
%Y A387133 Allowing repeated partitions gives A387327, see A299200, A357977.
%Y A387133 A000041 counts integer partitions, strict A000009.
%Y A387133 A003963 multiplies together prime indices.
%Y A387133 A112798 lists prime indices, row sums A056239 or A066328, lengths A001222.
%Y A387133 A120383 lists numbers divisible by all of their prime indices.
%Y A387133 A289509 lists numbers with relatively prime prime indices.
%Y A387133 Cf. A063834, A261049, A299201, A335433, A335448, A355739, A383706, A387111, A387135.
%K A387133 nonn,new
%O A387133 1,2
%A A387133 _Gus Wiseman_, Aug 26 2025