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%I #10 Sep 03 2018 23:05:15
%S 1,1,1,2,1,1,1,3,2,1,1,3,1,2,3,3,1,4,1,3,1,2,1,5,2,1,4,5,1,5,1,6,3,2,
%T 4,8,2,4,2,6,3,9,2,4,7,5,4,11,8,7,8,9,5,12,5,16,5,10,5,25,10,9,13,18,
%U 12,18,6,11,14,22,9,24,11,21,22,25,24,23,28,32
%N Number of integer partitions of n whose sum of reciprocals squared is the reciprocal of an integer.
%H Giovanni Resta, <a href="/A318586/b318586.txt">Table of n, a(n) for n = 1..150</a>
%e The a(42) = 9 integer partitions:
%e (42)
%e (21,14,7)
%e (18,9,9,6)
%e (18,9,9,3,3)
%e (20,10,4,4,4)
%e (12,12,12,4,2)
%e (10,5,5,5,5,5,5,2)
%e (12,6,6,4,4,4,2,2,2)
%e (6,6,4,4,4,4,3,3,3,3,2)
%t Table[Length[Select[IntegerPartitions[n],IntegerQ[1/Total[#^(-2)]]&]],{n,30}]
%Y Cf. A000041, A051908, A058360, A289506, A289507, A316854, A316857.
%Y Cf. A318584, A318585, A318587, A318588, A318589.
%K nonn
%O 1,4
%A _Gus Wiseman_, Aug 29 2018
%E a(61)-a(80) from _Giovanni Resta_, Sep 03 2018
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