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A326668
Number of strict factorizations of 2^n into factors > 1 with integer average.
5
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, 82, 118, 106, 149, 137, 213, 172, 263, 221, 363, 266, 453, 335, 594, 409, 735, 484, 968, 594, 1139, 731, 1486, 813, 1801, 1026, 2177, 1230, 2667, 1348, 3334, 1693
OFFSET
1,3
COMMENTS
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.
EXAMPLE
The a(1) = 1 through a(11) = 7 partitions (A = 10, B = 11):
(1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B)
(21) (31) (32) (42) (43) (53) (54) (64) (65)
(41) (51) (52) (62) (63) (73) (74)
(61) (71) (72) (82) (83)
(81) (91) (92)
(531) (A1)
(731)
MATHEMATICA
Table[Length[Select[IntegerPartitions[n], UnsameQ@@#&&IntegerQ[Mean[2^#]]&]], {n, 30}]
CROSSREFS
The non-strict case is A326667.
Factorizations with integer average are A326622.
Strict partitions with integer average are A102627.
Subsets with integer average are A051293.
Sequence in context: A366387 A083802 A325691 * A198318 A100881 A053263
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 17 2019
STATUS
approved