A319330 - OEIS

%I #7 Sep 19 2018 09:17:15

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%T 0,0,0,0,0,1,0,0,0,0,0,0,0,3,0,1,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,

%U 0,1,0,2,0,0,2,0,0,0,0,1,0,0,0,2,0,0,0,0,0,3,0,0,0,0,0,1,0,1,0,3,0,0,0,0,2

%N Number of integer partitions of n whose length is equal to the GCD of the parts and whose sum is equal to the LCM of the parts.

%e A list of all such partitions begins (1), (9,6,3), (20,8,8,4), (24,16,4,4), (16,16,12,4), (16,12,12,8), (25,10,5,5,5), (20,15,15,5,5), (20,15,10,10,5).

%t Table[Length[Select[IntegerPartitions[n],And[LCM@@#==Total[#],GCD@@#==Length[#]]&]],{n,30}]

%Y Cf. A067538, A074761, A143773, A316432, A319328, A319329, A319333.

%K nonn

%O 1,48

%A _Gus Wiseman_, Sep 17 2018

%E a(71)-a(105) from _Alois P. Heinz_, Sep 18 2018