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%I #7 Apr 16 2021 15:45:32
%S 1,0,0,0,0,1,1,2,3,4,6,8,9,13,18,21,26,32,38,47,57,66,80,95,110,132,
%T 157,181,211,246,282,327,379,435,500,570,648,743,849,963,1094,1241,
%U 1404,1592,1799,2025,2282,2568,2882,3239,3634,4066,4554,5094,5686,6346
%N Number of strict integer partitions of n with no part divisible by all the others.
%C Alternative name: Number of strict integer partitions of n that are empty or have greatest part not divisible by all the others.
%e The a(5) = 1 through a(12) = 9 partitions:
%e (3,2) (3,2,1) (4,3) (5,3) (5,4) (6,4) (6,5) (7,5)
%e (5,2) (4,3,1) (7,2) (7,3) (7,4) (5,4,3)
%e (5,2,1) (4,3,2) (5,3,2) (8,3) (6,4,2)
%e (5,3,1) (5,4,1) (9,2) (6,5,1)
%e (7,2,1) (5,4,2) (7,3,2)
%e (4,3,2,1) (6,4,1) (7,4,1)
%e (7,3,1) (8,3,1)
%e (5,3,2,1) (9,2,1)
%e (5,4,2,1)
%t Table[Length[Select[IntegerPartitions[n],#=={}||UnsameQ@@#&&!And@@IntegerQ/@(Max@@#/#)&]],{n,0,30}]
%Y The dual strict complement is A097986.
%Y The dual version is A341450.
%Y The non-strict version is A343341 (Heinz numbers: A343337).
%Y The strict complement is counted by A343347.
%Y The case with smallest part not divisible by all the others is A343379.
%Y The case with smallest part divisible by all the others is A343381.
%Y A000005 counts divisors.
%Y A000009 counts strict partitions.
%Y A000070 counts partitions with a selected part.
%Y A006128 counts partitions with a selected position.
%Y A015723 counts strict partitions with a selected part.
%Y A018818 counts partitions into divisors (strict: A033630).
%Y A167865 counts strict chains of divisors > 1 summing to n.
%Y A339564 counts factorizations with a selected factor.
%Y Cf. A083710, A130689, A200745, A264401, A338470, A339562, A343338, A343342, A343345, A343346, A343382.
%K nonn
%O 0,8
%A _Gus Wiseman_, Apr 16 2021
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