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%I #6 Dec 14 2018 21:20:26
%S 1,1,2,3,3,5,6,8,9,10,13,15,17,21,24,27,30,36,41,46,51,57,65,73,82,90,
%T 101,109,121,134,150,164,177,193,214,232,253,278,300,324,351,386,419,
%U 452,484,521,563,610,658,706,758,809,868,938,1006,1071,1140,1220,1307
%N Number of integer partitions of n whose product of parts is a squarefree number.
%C The parts of such a partition must also be squarefree and distinct except for any number of 1's.
%e The a(8) = 9 partitions are (53), (71), (521), (611), (5111), (32111), (311111), (2111111), (11111111). Missing from this list are (8), (62), (44), (431), (422), (4211), (41111), (332), (3311), (3221), (2222), (22211), (221111).
%t Table[Length[Select[IntegerPartitions[n],SquareFreeQ[Times@@#]&]],{n,30}]
%Y Partial sums of A322530.
%Y Cf. A001055, A003963, A005117, A064573 , A073576, A096276, A301987, A302505, A319005, A319916, A320322, A322527, A322529, A322531.
%K nonn
%O 0,3
%A _Gus Wiseman_, Dec 14 2018
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