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A328966 Number of strict factorizations of n with integer average.

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%I A328966 #4 Nov 16 2019 20:04:28
%S A328966 1,1,1,1,1,1,2,1,1,1,2,1,1,2,2,1,1,1,2,2,1,1,4,1,1,2,2,1,1,1,3,2,1,2,
%T A328966 2,1,1,2,3,1,2,1,2,3,1,1,5,1,1,2,2,1,1,2,3,2,1,1,5,1,1,3,3,2,1,1,2,2,
%U A328966 1,1,5,1,1,3,2,2,2,1,5,2,1,1,4,2,1,2,3
%N A328966 Number of strict factorizations of n with integer average.
%e A328966 The a(n) factorizations for n = 2, 8, 24, 48, 96:
%e A328966   (2)  (8)    (24)     (32)    (48)     (96)
%e A328966        (2*4)  (4*6)    (4*8)   (6*8)    (2*48)
%e A328966               (2*12)   (2*16)  (2*24)   (4*24)
%e A328966               (2*3*4)          (4*12)   (6*16)
%e A328966                                (2*4*6)  (8*12)
%e A328966                                         (3*4*8)
%e A328966                                         (2*3*16)
%e A328966                                         (2*4*12)
%t A328966 facs[n_]:=If[n<=1,{{}},Join@@Table[Map[Prepend[#,d]&,Select[facs[n/d],Min@@#>=d&]],{d,Rest[Divisors[n]]}]];
%t A328966 Table[Length[Select[facs[n],UnsameQ@@#&&IntegerQ[Mean[#]]&]],{n,2,100}]
%Y A328966 The non-strict version is A326622.
%Y A328966 Partitions with integer average are A067538.
%Y A328966 Strict partitions with integer average are A102627.
%Y A328966 Heinz numbers of partitions with integer average are A316413.
%Y A328966 Factorizations with integer geometric mean are A326028.
%Y A328966 Cf. A001055, A051293, A078174, A078175, A326515, A326567/A326568, A326619/A326620, A326621, A326625.
%K A328966 nonn
%O A328966 2,7
%A A328966 _Gus Wiseman_, Nov 16 2019