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%I #9 Dec 20 2020 14:50:16
%S 1,1,1,1,1,1,2,1,1,1,1,1,4,1,1,2,3,1,5,1,6,1,1,1,16,1,1,1,12,1,33,1,
%T 15,1,1,1,60,1,1,1,51,1,81,1,31,57,1,1,216,1,55,1,45,1,230,1,223,1,1,
%U 1,800,1,1,314,273,1,607,1,81,1,315,1,2404,1,1,319
%N Number of strict integer partitions of n whose length and maximum both divide n.
%H Fausto A. C. Cariboni, <a href="/A326851/b326851.txt">Table of n, a(n) for n = 0..383</a>
%e The a(6) = 2 through a(24) = 16 partitions (1 terms not shown):
%e 6 12 15 16 18 20 24
%e 3,2,1 6,4,2 5,4,3,2,1 8,4,3,1 9,5,4 10,5,3,2 12,7,5
%e 6,5,1 8,5,2,1 9,6,3 10,5,4,1 12,8,4
%e 6,3,2,1 9,7,2 10,6,3,1 12,9,3
%e 9,8,1 10,7,2,1 12,10,2
%e 10,4,3,2,1 12,11,1
%e 8,7,5,4
%e 8,7,6,3
%e 12,5,4,3
%e 12,6,4,2
%e 12,6,5,1
%e 12,7,3,2
%e 12,7,4,1
%e 12,8,3,1
%e 12,9,2,1
%e 8,6,4,3,2,1
%t Table[If[n==0,1,Length[Select[IntegerPartitions[n],UnsameQ@@#&&Divisible[n,Max[#]]&&Divisible[n,Length[#]]&]]],{n,0,30}]
%Y The non-strict case is A326843.
%Y Cf. A018818, A047993, A067538, A326837, A326842, A326849, A326852.
%K nonn
%O 0,7
%A _Gus Wiseman_, Jul 26 2019
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