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%I #8 Aug 30 2018 08:36:56
%S 0,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,0,0,1,1,0,0,0,1,0,
%T 0,0,1,0,1,1,0,2,2,0,0,0,2,0,2,1,2,2,2,1,1,2,3,0,1,1,6,2,3,2,6,2,2,3,
%U 2,6,7,2,4,3,9,4,7,5,8,8,7,9,9,11,12,7,9,11,17,9,13,12,17,16,13,15,20,26,27,18,23
%N Number of integer partitions of n whose sum of reciprocals squared is 1.
%C The a(16) = 1 integer partition:
%C (6,3,3,2,2,2)
%C The a(48) = 2 integer partitions:
%C (18,9,9,3,3,2,2,2)
%C (6,6,6,6,3,3,3,3,3,3,3,3)
%C The a(56) = 3 integer partitions:
%C (12,6,6,4,4,4,4,4,4,4,2,2)
%C (10,6,5,5,5,5,5,5,3,3,2,2)
%C (6,6,4,4,4,4,4,4,4,4,3,3,3,3)
%C The a(60) = 6 integer partitions:
%C (12,12,12,12,3,3,2,2,2)
%C (8,8,8,8,6,4,4,4,3,3,2,2)
%C (6,6,6,6,6,6,6,6,6,2,2,2)
%C (12,12,12,4,3,3,3,3,3,3,2)
%C (10,5,5,5,5,5,5,4,4,4,4,2,2)
%C (6,4,4,4,4,4,4,4,4,4,4,4,4,3,3)
%t Table[Length[Select[IntegerPartitions[n],Total[#^(-2)]==1&]],{n,30}]
%Y Cf. A000041, A051908, A058360, A289506, A289507, A316854, A316855.
%Y Cf. A318585, A318586, A318587, A318588, A318589.
%K nonn
%O 0,42
%A _Gus Wiseman_, Aug 29 2018
%E a(61)-a(100) from _Alois P. Heinz_, Aug 30 2018