cp's OEIS Frontend

A343377 Number of strict integer partitions of n with no part divisible by all the others.

%I A343377 #7 Apr 16 2021 15:45:32
%S A343377 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 A343377 157,181,211,246,282,327,379,435,500,570,648,743,849,963,1094,1241,
%U A343377 1404,1592,1799,2025,2282,2568,2882,3239,3634,4066,4554,5094,5686,6346
%N A343377 Number of strict integer partitions of n with no part divisible by all the others.
%C A343377 Alternative name: Number of strict integer partitions of n that are empty or have greatest part not divisible by all the others.
%e A343377 The a(5) = 1 through a(12) = 9 partitions:
%e A343377   (3,2)  (3,2,1)  (4,3)  (5,3)    (5,4)    (6,4)      (6,5)      (7,5)
%e A343377                   (5,2)  (4,3,1)  (7,2)    (7,3)      (7,4)      (5,4,3)
%e A343377                          (5,2,1)  (4,3,2)  (5,3,2)    (8,3)      (6,4,2)
%e A343377                                   (5,3,1)  (5,4,1)    (9,2)      (6,5,1)
%e A343377                                            (7,2,1)    (5,4,2)    (7,3,2)
%e A343377                                            (4,3,2,1)  (6,4,1)    (7,4,1)
%e A343377                                                       (7,3,1)    (8,3,1)
%e A343377                                                       (5,3,2,1)  (9,2,1)
%e A343377                                                                  (5,4,2,1)
%t A343377 Table[Length[Select[IntegerPartitions[n],#=={}||UnsameQ@@#&&!And@@IntegerQ/@(Max@@#/#)&]],{n,0,30}]
%Y A343377 The dual strict complement is A097986.
%Y A343377 The dual version is A341450.
%Y A343377 The non-strict version is A343341 (Heinz numbers: A343337).
%Y A343377 The strict complement is counted by A343347.
%Y A343377 The case with smallest part not divisible by all the others is A343379.
%Y A343377 The case with smallest part divisible by all the others is A343381.
%Y A343377 A000005 counts divisors.
%Y A343377 A000009 counts strict partitions.
%Y A343377 A000070 counts partitions with a selected part.
%Y A343377 A006128 counts partitions with a selected position.
%Y A343377 A015723 counts strict partitions with a selected part.
%Y A343377 A018818 counts partitions into divisors (strict: A033630).
%Y A343377 A167865 counts strict chains of divisors > 1 summing to n.
%Y A343377 A339564 counts factorizations with a selected factor.
%Y A343377 Cf. A083710, A130689, A200745, A264401, A338470, A339562, A343338, A343342, A343345, A343346, A343382.
%K A343377 nonn
%O A343377 0,8
%A A343377 _Gus Wiseman_, Apr 16 2021