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%I #16 Dec 25 2020 04:20:32
%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,
%T 0,0,1,0,0,0,2,0,2,0,0,0,2,0,2,0,1,0,4,0,3,0,1,0,5,0,8,0,2,0,5,0,10,0,
%U 4,0,13,0,15,0,3,1,13,0,19,0,9,1,24,0,20
%N Number of strict integer partitions of n with relatively prime parts in which no two parts are relatively prime.
%H Fausto A. C. Cariboni, <a href="/A318715/b318715.txt">Table of n, a(n) for n = 1..500</a>
%e The a(67) = 10 strict integer partitions are
%e (45,12,10) (42,15,10) (40,15,12) (33,22,12) (28,21,18)
%e (36,15,10,6) (30,15,12,10) (28,21,12,6) (24,18,15,10)
%e (24,15,12,10,6).
%t Table[Length[Select[IntegerPartitions[n],And[UnsameQ@@#,GCD@@#==1,And@@(GCD[##]>1&)@@@Select[Tuples[#,2],Less@@#&]]&]],{n,50}]
%Y Cf. A007359, A051185, A078374, A303140, A303282, A303283, A305713, A305843, A305854, A318716, A318717, A318720.
%K nonn
%O 1,41
%A _Gus Wiseman_, Sep 02 2018
%E a(71)-a(85) from _Robert Price_, Sep 08 2018
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