A326622 - OEIS

%I #5 Jul 15 2019 01:44:48

%S 1,1,2,1,1,1,3,2,1,1,2,1,1,2,4,1,1,1,3,2,1,1,4,2,1,3,2,1,1,1,5,2,1,2,

%T 3,1,1,2,3,1,2,1,3,3,1,1,6,2,2,2,2,1,2,2,4,2,1,1,6,1,1,3,7,2,1,1,3,2,

%U 1,1,6,1,1,3,2,2,2,1,7,5,1,1,4,2,1,2,3

%N Number of factorizations of n into factors > 1 with integer average.

%e The a(80) = 7 factorizations:

%e   (2*2*2*10)

%e   (2*2*20)

%e   (2*5*8)

%e   (2*40)

%e   (4*20)

%e   (8*10)

%e   (80)

%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],IntegerQ[Mean[#]]&]],{n,2,100}]

%Y Partitions with integer average are A067538.

%Y Strict partitions with integer average are A102627.

%Y Heinz numbers of partitions with integer average are A316413.

%Y Factorizations with integer geometric mean are A326028.

%Y Cf. A001055, A051293, A078174, A078175, A326514, A326515, A326567/A326568, A326621, A326623.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jul 14 2019