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%I #4 Jul 18 2019 06:18:41
%S 1,1,2,2,3,3,4,4,6,5,7,7,9,9,12,12,17,17,21,24,33,33,42,46,63,61,81,
%T 82,118,106,149,137,213,172,263,221,363,266,453,335,594,409,735,484,
%U 968,594,1139,731,1486,813,1801,1026,2177,1230,2667,1348,3334,1693
%N Number of strict factorizations of 2^n into factors > 1 with integer average.
%C Also the number of strict integer partitions y of n such that the average of the set {2^s: s in y} is an integer.
%e The a(1) = 1 through a(11) = 7 partitions (A = 10, B = 11):
%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
%e (21) (31) (32) (42) (43) (53) (54) (64) (65)
%e (41) (51) (52) (62) (63) (73) (74)
%e (61) (71) (72) (82) (83)
%e (81) (91) (92)
%e (531) (A1)
%e (731)
%t Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&IntegerQ[Mean[2^#]]&]],{n,30}]
%Y The non-strict case is A326667.
%Y Factorizations with integer average are A326622.
%Y Strict partitions with integer average are A102627.
%Y Subsets with integer average are A051293.
%Y Cf. A001055, A067538, A102627, A326028, A326647, A326666, A326670, A326671.
%K nonn
%O 1,3
%A _Gus Wiseman_, Jul 17 2019
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