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%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
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