cp's OEIS Frontend

A338553 Number of integer partitions of n that are either constant or relatively prime.

%I A338553 #11 Nov 05 2020 22:57:03
%S A338553 1,1,2,3,5,7,10,15,20,29,37,56,68,101,122,170,213,297,352,490,587,778,
%T A338553 948,1255,1488,1953,2337,2983,3585,4565,5393,6842,8123,10088,12015,
%U A338553 14865,17534,21637,25527,31085,36701,44583,52262,63261,74175,88936,104305,124754
%N A338553 Number of integer partitions of n that are either constant or relatively prime.
%C A338553 The Heinz numbers of these partitions are given by A338555 = A000961 \/ A289509. The Heinz number of a partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k), giving a bijective correspondence between positive integers and integer partitions.
%F A338553 For n > 0, a(n) = A000005(n) + A000837(n) - 1.
%e A338553 The a(1) = 1 through a(7) = 15 partitions:
%e A338553   (1)  (2)   (3)    (4)     (5)      (6)       (7)
%e A338553        (11)  (21)   (22)    (32)     (33)      (43)
%e A338553              (111)  (31)    (41)     (51)      (52)
%e A338553                     (211)   (221)    (222)     (61)
%e A338553                     (1111)  (311)    (321)     (322)
%e A338553                             (2111)   (411)     (331)
%e A338553                             (11111)  (2211)    (421)
%e A338553                                      (3111)    (511)
%e A338553                                      (21111)   (2221)
%e A338553                                      (111111)  (3211)
%e A338553                                                (4111)
%e A338553                                                (22111)
%e A338553                                                (31111)
%e A338553                                                (211111)
%e A338553                                                (1111111)
%t A338553 Table[Length[Select[IntegerPartitions[n],SameQ@@#||GCD@@#==1&]],{n,0,30}]
%Y A338553 A023022(n) + A059841(n) is the 2-part version.
%Y A338553 A078374(n) + 1 is the strict case (n > 1).
%Y A338553 A338554 counts the complement, with Heinz numbers A338552.
%Y A338553 A338555 gives the Heinz numbers of these partitions.
%Y A338553 A000005 counts constant partitions, with Heinz numbers A000961.
%Y A338553 A000837 counts relatively prime partitions, with Heinz numbers A289509.
%Y A338553 A282750 counts relatively prime partitions by sum and length.
%Y A338553 Cf. A000010, A007360, A008284, A023023, A051424, A101271, A101391, A302698, A304712, A327516, A337664.
%K A338553 nonn
%O A338553 0,3
%A A338553 _Gus Wiseman_, Nov 03 2020