A326668 Number of strict factorizations of 2^n into factors > 1 with integer average.

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.

Links

Table of n, a(n) for n=1..58.

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.

Cf. A001055, A067538, A102627, A326028, A326647, A326666, A326670, A326671.

Sequence in context: A366387 A083802 A325691 * A198318 A100881 A053263

Adjacent sequences: A326665 A326666 A326667 * A326669 A326670 A326671

Keyword

nonn

Author

Gus Wiseman, Jul 17 2019

Status

approved