A326667 - OEIS

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A326667

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

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

(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: s in y} is an integer.

LINKS

Table of n, a(n) for n=1..51.

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.

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

Sequence in context: A366064 A238484 A241340 * A293441 A306203 A111795

Adjacent sequences: A326664 A326665 A326666 * A326668 A326669 A326670

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 17 2019

STATUS

approved