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%I #5 Jul 18 2019 06:19:03
%S 1,2,2,3,4,5,7,8,11,14,14,20,27,31,41,47,57,75,95,102,155,170,195,239,
%T 327,331,483,517,617,740,952,942,1406,1484,1742,2023,2652,2688,3680,
%U 3892,4729,5375,6689,6911,9437,9938,11754,13529,16710,17419,22346,24230
%N Number of factorizations of 2^n into factors > 1 with even integer average.
%C Also the number of integer partitions y of n such that the average of the multiset {2^(s - 1): s in y} is an integer.
%e The a(1) = 1 through a(8) = 8 partitions:
%e (1) (2) (3) (4) (5) (6) (7) (8)
%e (11) (111) (22) (32) (33) (43) (44)
%e (1111) (311) (42) (52) (53)
%e (11111) (222) (331) (62)
%e (111111) (511) (422)
%e (3211) (2222)
%e (1111111) (4211)
%e (11111111)
%t Table[Length[Select[IntegerPartitions[n],IntegerQ[Mean[2^(#-1)]]&]],{n,30}]
%Y The strict case is A326670.
%Y Factorizations with integer average are A326622.
%Y Partitions with integer average are A067538.
%Y Cf. A001055, A051293, A102627, A326028, A326622, A326647, A326666, A326667, A326668.
%K nonn
%O 1,2
%A _Gus Wiseman_, Jul 17 2019
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