A316440 - OEIS

%I #15 Sep 03 2023 08:46:39

%S 1,1,2,2,4,2,6,2,7,5,8,2,13,2,10,10,14,2,20,2,17,15,14,2,32,3,16,22,

%T 25,2,40,2,27,30,20,4,58,2,22,40,40,2,64,2,40,53,26,2,93,3,30,64,54,2,

%U 94,4,58,78,32,2,138,2,34,96,75,10,131,2,76,111,48,2,192,2,40,138,99

%N Number of integer partitions of n such that every submultiset has an integer average.

%H Max Alekseyev, <a href="/A316440/b316440.txt">Table of n, a(n) for n = 0..500</a>

%F For a prime p, a(p) = 2. - _Max Alekseyev_, Sep 02 2023

%e The a(12) = 13 partitions:

%e   (12),

%e   (6,6), (7,5), (8,4), (9,3), (10,2), (11,1),

%e   (4,4,4), (6,4,2), (8,2,2),

%e   (3,3,3,3),

%e   (2,2,2,2,2,2),

%e   (1,1,1,1,1,1,1,1,1,1,1,1).

%t Table[Length[Select[IntegerPartitions[n],And@@IntegerQ/@Mean/@Union[Rest[Subsets[#]]]&]],{n,20}]

%Y Cf. A067538, A074761, A122768, A143773, A237984, A298423, A316313, A316314.

%K nonn

%O 0,3

%A _Gus Wiseman_, Jul 03 2018

%E a(0) prepended and more terms added by _Max Alekseyev_, Sep 02 2023