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%I #7 Jul 16 2018 21:47:48
%S 1,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,1,0,0,0,0,2,0,0,0,0,0,1,3,1,2,1,1,1,
%T 2,1,5,3,1,1,5,2,9,3,3,3,4,2,6,6,3,4,9,5,10,5,10,9,15,10,21,12,14,16,
%U 18,9,30,18,17,17,28,16,29,26,26,30,28,33,48,31
%N Number of integer partitions of n into relatively prime parts whose reciprocal sum is 1.
%C The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.
%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>
%e The a(43) = 9 partitions:
%e (24,8,4,4,3)
%e (21,7,7,6,2)
%e (20,12,5,3,3)
%e (20,8,8,5,2)
%e (15,15,6,5,2)
%e (15,12,10,4,2)
%e (14,7,7,7,4,4)
%e (12,8,8,6,6,3)
%e (10,10,10,5,4,4).
%t Table[Length[Select[IntegerPartitions[n],And[GCD@@#==1,Sum[1/m,{m,#}]==1]&]],{n,30}]
%Y Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316888-A316904.
%K nonn
%O 1,22
%A _Gus Wiseman_, Jul 16 2018
%E a(71)-a(80) from _Giovanni Resta_, Jul 16 2018
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