cp's OEIS Frontend

A339619 Number of integer partitions of n with no 1's and a part divisible by all the other parts.

%I A339619 #10 Apr 22 2021 01:42:23
%S A339619 1,0,1,1,2,1,4,1,5,3,7,2,13,2,13,9,17,6,27,7,33,19,35,16,58,22,58,39,
%T A339619 75,37,108,44,117,75,132,88,190,94,199,147,250,153,322,180,363,271,
%U A339619 405,286,544,339,601,458,699,503,868,608,990,777,1113,865,1422,993
%N A339619 Number of integer partitions of n with no 1's and a part divisible by all the other parts.
%C A339619 Alternative name: Number of integer partitions of n with no 1's that are empty or have greatest part divisible by all the other parts.
%e A339619 The a(6) = 4 through a(16) = 17 partitions (A..G = 10..16):
%e A339619   6    7  8     9    A      B    C       D     E        F      G
%e A339619   33      44    63   55     632  66      6322  77       A5     88
%e A339619   42      62    333  82          84            C2       C3     C4
%e A339619   222     422        442         93            662      555    E2
%e A339619           2222       622         A2            842      663    844
%e A339619                      4222        444           A22      933    C22
%e A339619                      22222       633           4442     6333   4444
%e A339619                                  822           6332     33333  6622
%e A339619                                  3333          8222     63222  8422
%e A339619                                  4422          44222           A222
%e A339619                                  6222          62222           44422
%e A339619                                  42222         422222          63322
%e A339619                                  222222        2222222         82222
%e A339619                                                                442222
%e A339619                                                                622222
%e A339619                                                                4222222
%e A339619                                                                22222222
%t A339619 Table[If[n==0,1,Length[Select[IntegerPartitions[n],FreeQ[#,1]&&Or@@And@@IntegerQ/@(Max@@#/#)&]]],{n,0,30}]
%Y A339619 The dual version is A083711.
%Y A339619 The version with 1's allowed is A130689.
%Y A339619 The strict case is A339660.
%Y A339619 The Heinz numbers of these partitions are the odd complement of A343337.
%Y A339619 The strict case with 1's allowed is A343347.
%Y A339619 A000009 counts strict partitions.
%Y A339619 A000041 counts partitions.
%Y A339619 A000070 counts partitions with a selected part.
%Y A339619 A006128 counts partitions with a selected position.
%Y A339619 A015723 counts strict partitions with a selected part.
%Y A339619 Cf. A066186, A083710, A083711, A097986, A130714, A338470, A343341, A343342, A343346, A343377, A343382.
%K A339619 nonn
%O A339619 0,5
%A A339619 _Gus Wiseman_, Apr 18 2021