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%I #6 May 13 2019 08:11:51
%S 1,1,1,2,2,2,2,3,3,3,4,5,5,5,6,7,7,8,9,10,10,11,12,14,14,15,16,18,19,
%T 20,22,24,25,26,28,31,33,34,36,39,41,43,45,49,52,54,57,61,65,68,71,76,
%U 80,84,88,93,98,103,107,113
%N Number of integer partitions of n whose reciprocal factorial sum is an integer.
%C The reciprocal factorial sum of an integer partition (y_1,...,y_k) is 1/y_1! + ... + 1/y_k!.
%e The initial terms count the following partitions:
%e 1: (1)
%e 2: (1,1)
%e 3: (1,1,1)
%e 4: (2,2)
%e 4: (1,1,1,1)
%e 5: (2,2,1)
%e 5: (1,1,1,1,1)
%e 6: (2,2,1,1)
%e 6: (1,1,1,1,1,1)
%e 7: (2,2,1,1,1)
%e 7: (1,1,1,1,1,1,1)
%e 8: (2,2,2,2)
%e 8: (2,2,1,1,1,1)
%e 8: (1,1,1,1,1,1,1,1)
%e 9: (2,2,2,2,1)
%e 9: (2,2,1,1,1,1,1)
%e 9: (1,1,1,1,1,1,1,1,1)
%t Table[Length[Select[IntegerPartitions[n],IntegerQ[Total[1/(#!)]]&]],{n,30}]
%Y Factorial numbers: A000142, A007489, A022559, A064986, A108731, A115944, A284605, A325508, A325616.
%Y Reciprocal factorial sum: A002966, A051908, A058360, A316854, A316856, A325618, A325621, A325622.
%K nonn,more
%O 1,4
%A _Gus Wiseman_, May 13 2019
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