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 A326671 Number of factorizations of 2^n into factors > 1 with even integer average. 5
 1, 2, 2, 3, 4, 5, 7, 8, 11, 14, 14, 20, 27, 31, 41, 47, 57, 75, 95, 102, 155, 170, 195, 239, 327, 331, 483, 517, 617, 740, 952, 942, 1406, 1484, 1742, 2023, 2652, 2688, 3680, 3892, 4729, 5375, 6689, 6911, 9437, 9938, 11754, 13529, 16710, 17419, 22346, 24230 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE The a(1) = 1 through a(8) = 8 partitions:   (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)        (11)  (111)  (22)    (32)     (33)      (43)       (44)                     (1111)  (311)    (42)      (52)       (53)                             (11111)  (222)     (331)      (62)                                      (111111)  (511)      (422)                                                (3211)     (2222)                                                (1111111)  (4211)                                                           (11111111) MATHEMATICA Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[2^(#-1)]]&]], {n, 30}] CROSSREFS The strict case is A326670. Factorizations with integer average are A326622. Partitions with integer average are A067538. Cf. A001055, A051293, A102627, A326028, A326622, A326647, A326666, A326667, A326668. Sequence in context: A304329 A111901 A316202 * A134727 A152305 A131419 Adjacent sequences:  A326668 A326669 A326670 * A326672 A326673 A326674 KEYWORD nonn AUTHOR Gus Wiseman, Jul 17 2019 STATUS approved

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Last modified May 7 10:46 EDT 2021. Contains 343650 sequences. (Running on oeis4.)