A326670 - OEIS

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.

%I #4 Jul 18 2019 06:18:56

%S 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,

%T 74,75,90,99,133,127,158,167,226,203,278,262,371,325,457,387,622,484,

%U 715,606,969,672,1178,866,1428,1050,1776,1142,2276,1459,2514,1792

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

%e The a(1) = 1 through a(12) = 6 partitions (A = 10, B = 11, C = 12):

%e (1) (2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)

%e (32) (42) (43) (53) (54) (64) (65) (75)

%e (52) (62) (63) (73) (74) (84)

%e (72) (82) (83) (93)

%e (531) (92) (A2)

%e (731) (642)

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

%Y The non-strict case is A326671.

%Y Strict factorizations with integer average are A326668.

%Y Strict partitions with integer average are A102627.

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

%K nonn

%O 1,5

%A _Gus Wiseman_, Jul 17 2019