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%I #8 Jul 16 2018 21:47:23
%S 1,1,1,1,1,1,1,1,2,2,2,1,1,1,1,2,2,2,1,4,1,5,1,2,3,2,4,5,5,5,4,3,5,4,
%T 8,6,9,7,5,6,10,6,12,8,7,7,6,6,12,12,8,18,13,16,19,17,18,21,26,26,28,
%U 29,21,29,29,27,38,32,26,37,32,38,39,49,36,61,46,55
%N Number of aperiodic integer partitions of n whose reciprocal sum is the reciprocal of an integer.
%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>
%t Table[Length[Select[IntegerPartitions[n],And[GCD@@Length/@Split[#]==1,IntegerQ[1/Sum[1/m,{m,#}]]]&]],{n,30}]
%Y Cf. A000837, A002966, A051908, A058360, A100953, A316854, A316857, A316888-A316904.
%K nonn
%O 1,9
%A _Gus Wiseman_, Jul 16 2018
%E a(51)-a(78) from _Giovanni Resta_, Jul 16 2018
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