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A326667
Number of factorizations of 2^n into factors > 1 with integer average.
6
1, 2, 3, 4, 5, 7, 8, 11, 15, 19, 21, 29, 37, 44, 58, 67, 86, 105, 136, 146, 219, 236, 295, 327, 473, 469, 694, 707, 932, 1020, 1398, 1340, 2023, 2059, 2636, 2816, 3887, 3855, 5377, 5467, 7095, 7611, 9924, 9992, 13795, 14205, 17728, 19315, 24803, 25452, 33026
OFFSET
1,2
COMMENTS
Also the number of integer partitions y of n such that the average of the multiset {2^s: s in y} is an integer.
EXAMPLE
The a(1) = 1 through a(8) = 11 partitions:
(1) (2) (3) (4) (5) (6) (7) (8)
(11) (21) (22) (32) (33) (43) (44)
(111) (31) (41) (42) (52) (53)
(1111) (311) (51) (61) (62)
(11111) (222) (331) (71)
(2211) (511) (422)
(111111) (3211) (2222)
(1111111) (3311)
(4211)
(311111)
(11111111)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], IntegerQ[Mean[2^#]]&]], {n, 30}]
CROSSREFS
The strict case is A326668.
Factorizations with integer average are A326622.
Partitions with integer average are A067538.
Subsets with integer average are A051293.
Sequence in context: A366064 A238484 A241340 * A293441 A306203 A111795
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved