A325620 - OEIS

%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