A326670 Number of strict integer partitions y of n such that the average of the set {2^(s - 1): s in y} is an integer.

1, 1, 1, 1, 2, 2, 3, 3, 5, 4, 6, 6, 8, 7, 10, 9, 13, 12, 15, 16, 23, 22, 27, 31, 41, 41, 50, 57, 74, 75, 90, 99, 133, 127, 158, 167, 226, 203, 278, 262, 371, 325, 457, 387, 622, 484, 715, 606, 969, 672, 1178, 866, 1428, 1050, 1776, 1142, 2276, 1459, 2514, 1792

Offset: 1

Author

Gus Wiseman, Jul 17 2019

Keywords

• nonn

Examples

			The a(1) = 1 through a(12) = 6 partitions (A = 10, B = 11, C = 12):
  (1)  (2)  (3)  (4)  (5)   (6)   (7)   (8)   (9)    (A)   (B)    (C)
                      (32)  (42)  (43)  (53)  (54)   (64)  (65)   (75)
                                  (52)  (62)  (63)   (73)  (74)   (84)
                                              (72)   (82)  (83)   (93)
                                              (531)        (92)   (A2)
                                                           (731)  (642)
		

Crossrefs

The non-strict case is A326671.

Strict factorizations with integer average are A326668.

Strict partitions with integer average are A102627.

Cf. A001055, A051293, A067538, A102627, A326028, A326622, A326647, A326666, A326667.

Programs

Mathematica

Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&IntegerQ[Mean[2^(#-1)]]&]],{n,30}]