A325720 Number of separable partitions of n in which the number of distinct (repeatable) parts is > 5.
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 10, 20, 36, 64, 101, 166, 254, 388, 568, 830, 1169, 1645, 2270, 3096, 4161, 5556, 7312, 9572, 12402, 15962, 20386, 25851, 32595, 40850, 50938, 63148, 77979, 95773, 117231, 142777, 173387
Offset: 1
Programs
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Mathematica
(separable=Table[Map[#[[1]]&,Select[Map[{#,Quotient[(1+Length[#]),Max[Map[Length,Split[#]]]]}&,IntegerPartitions[nn]],#[[2]]>1&]],{nn,35}]); Map[Length[Select[Map[{#,Length[Union[#]]}&,#],#[[2]]>5&]]&,separable] (* Peter J. C. Moses, May 08 2019 *)
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