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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
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.
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.
Sequence in context: A304329 A111901 A316202 * A134727 A152305 A131419
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved