This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A326671 #5 Jul 18 2019 06:19:03
%S A326671 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 A326671 327,331,483,517,617,740,952,942,1406,1484,1742,2023,2652,2688,3680,
%U A326671 3892,4729,5375,6689,6911,9437,9938,11754,13529,16710,17419,22346,24230
%N A326671 Number of factorizations of 2^n into factors > 1 with even integer average.
%C A326671 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 A326671 The a(1) = 1 through a(8) = 8 partitions:
%e A326671 (1) (2) (3) (4) (5) (6) (7) (8)
%e A326671 (11) (111) (22) (32) (33) (43) (44)
%e A326671 (1111) (311) (42) (52) (53)
%e A326671 (11111) (222) (331) (62)
%e A326671 (111111) (511) (422)
%e A326671 (3211) (2222)
%e A326671 (1111111) (4211)
%e A326671 (11111111)
%t A326671 Table[Length[Select[IntegerPartitions[n],IntegerQ[Mean[2^(#-1)]]&]],{n,30}]
%Y A326671 The strict case is A326670.
%Y A326671 Factorizations with integer average are A326622.
%Y A326671 Partitions with integer average are A067538.
%Y A326671 Cf. A001055, A051293, A102627, A326028, A326622, A326647, A326666, A326667, A326668.
%K A326671 nonn
%O A326671 1,2
%A A326671 _Gus Wiseman_, Jul 17 2019