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%I #5 Apr 21 2018 20:57:54
%S 0,0,0,0,1,1,5,6,13,17,33,37,68,82,125,159,237,278,409,491,674,830,
%T 1121,1329,1781,2144,2770,3345,4299,5086,6507,7752,9687,11571,14378,
%U 16985,21039,24876,30379,35924,43734,51320,62238,73068,87747,103021,123347,143955
%N Number of integer partitions of n with at least two but not all parts having a common divisor greater than 1.
%e The a(7) = 5 partitions are (421), (331), (322), (2221), (22111).
%t Table[Select[IntegerPartitions[n],!CoprimeQ@@#&&GCD@@#===1&]//Length,{n,30}]
%Y Cf. A000837, A018783, A051424, A078374, A168532, A289508, A289509, A298748, A300486, A302569, A302696, A302796, A303138, A303140.
%K nonn
%O 1,7
%A _Gus Wiseman_, Apr 19 2018
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