%I #6 Sep 10 2018 06:11:56

%S 1,2,3,4,6,8,12,18,24,36,54,72,108,162,216,324,486,648,972,1458,1944,

%T 2916,4374,5832,8748,13122,17496,26244,39366,52488,78732,118098,

%U 157464,236196,354294,472392,708588,1062882,1417176,2125764,3188646,4251528,6377292

%N Maximum product of an aperiodic integer partition of n.

%C An integer partition is aperiodic if its multiplicities are relatively prime.

%e Among the aperiodic partitions of 9, those with maximum product are (432) and (3222), so a(9) = 24. If periodic partitions were allowed, we would have (333) with product 27.

%t Table[Max[Times@@@Select[IntegerPartitions[n],GCD@@Length/@Split[#]==1&]],{n,30}]

%Y Cf. A000740, A000792, A000793, A000837, A007916, A100953, A281116, A289508, A289509, A296302.

%K nonn

%O 1,2

%A _Gus Wiseman_, Sep 09 2018