%I #7 Jul 16 2018 21:47:42

%S 1,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,1,0,0,1,0,3,0,1,0,1,1,2,3,2,2,1,2,2,

%T 2,3,5,5,2,2,5,5,9,3,4,6,4,3,6,8,4,10,9,8,11,7,13,12,15,15,21,18,16,

%U 21,19,17,30,23,19,23,28,25,29,34,29,44,28,46,48,42

%N Number of aperiodic integer partitions of n whose reciprocal sum is 1.

%C The reciprocal sum of (y_1, ..., y_k) is 1/y_1 + ... + 1/y_k.

%C A partition is aperiodic if its multiplicities are relatively prime.

%H Gus Wiseman, <a href="/A051908/a051908.txt">Sequences counting and ranking integer partitions by their reciprocal sums</a>

%e The a(37) = 5 partitions are (24,8,3,2), (20,5,4,4,4), (15,10,6,3,3), (14,7,7,7,2), (10,10,10,5,2).

%t Table[Length[Select[IntegerPartitions[n],And[GCD@@Length/@Split[#]==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(51)-a(80) from _Giovanni Resta_, Jul 16 2018