cp's OEIS Frontend

A339660 Number of strict integer partitions of n with no 1's and a part divisible by all the other parts.

%I A339660 #12 Apr 22 2021 01:42:31
%S A339660 1,0,1,1,1,1,2,1,2,2,2,2,4,1,3,3,3,3,5,2,5,5,4,5,7,3,5,6,5,5,9,4,7,6,
%T A339660 6,9,11,6,9,10,9,10,12,6,11,12,10,12,16,9,15,16,12,14,18,14,16,18,14,
%U A339660 15,22,11,16,20,13,21,23,15,21,24,21,21,31,14,24
%N A339660 Number of strict integer partitions of n with no 1's and a part divisible by all the other parts.
%C A339660 Alternative name: Number of strict integer partitions of n with no 1's that are empty or have greatest part divisible by all the other parts.
%e A339660 The a(n) partitions for n = 14, 12, 18, 24, 30, 39, 36:
%e A339660   (14)     (12)    (18)      (24)        (30)        (39)          (36)
%e A339660   (12,2)   (8,4)   (12,6)    (16,8)      (24,6)      (36,3)        (27,9)
%e A339660   (8,4,2)  (9,3)   (15,3)    (18,6)      (25,5)      (26,13)       (30,6)
%e A339660            (10,2)  (16,2)    (20,4)      (27,3)      (27,9,3)      (32,4)
%e A339660                    (12,4,2)  (21,3)      (28,2)      (28,7,4)      (33,3)
%e A339660                              (22,2)      (20,10)     (30,6,3)      (34,2)
%e A339660                              (12,6,4,2)  (18,9,3)    (24,12,3)     (24,12)
%e A339660                                          (24,4,2)    (24,8,4,3)    (24,8,4)
%e A339660                                          (16,8,4,2)  (20,10,5,4)   (18,9,6,3)
%e A339660                                                      (24,6,4,3,2)  (24,6,4,2)
%e A339660                                                                    (20,10,4,2)
%t A339660 Table[If[n==0,1,Length[Select[IntegerPartitions[n],FreeQ[#,1]&&UnsameQ@@#&&And@@IntegerQ/@(Max@@#/#)&]]],{n,0,30}]
%Y A339660 The dual version is A098965 (non-strict: A083711).
%Y A339660 The non-strict version is A339619 (Heinz numbers: complement of A343337).
%Y A339660 The version with 1's allowed is A343347 (non-strict: A130689).
%Y A339660 The case without a part dividing all the other parts is A343380.
%Y A339660 A000009 counts strict partitions.
%Y A339660 A000070 counts partitions with a selected part.
%Y A339660 A015723 counts strict partitions with a selected part.
%Y A339660 A018818 counts partitions into divisors (strict: A033630).
%Y A339660 A167865 counts strict chains of divisors > 1 summing to n.
%Y A339660 Cf. A083710, A097986, A098743, A200745, A264401, A339563, A341450, A343337, A343341, A343344, A343378.
%K A339660 nonn
%O A339660 0,7
%A A339660 _Gus Wiseman_, Apr 19 2021