A323053 Number of integer partitions of n with no 1's such that no part is a power of any other (unequal) part.

1, 0, 1, 1, 2, 2, 3, 4, 6, 7, 9, 12, 15, 19, 25, 30, 38, 47, 58, 71, 87, 106, 131, 156, 190, 228, 275, 328, 394, 468, 556, 661, 784, 923, 1089, 1283, 1507, 1766, 2068, 2416, 2821, 3284, 3822, 4438, 5148, 5961, 6898, 7968, 9195, 10593, 12198, 14019, 16102, 18472

Offset: 0

Author

Gus Wiseman, Jan 04 2019

Keywords

• nonn

Examples

			The a(2) = 1 through a(11) = 12 integer partitions (A = 10, B = 11):
  (2)  (3)  (4)   (5)   (6)    (7)    (8)     (9)     (A)      (B)
            (22)  (32)  (33)   (43)   (44)    (54)    (55)     (65)
                        (222)  (52)   (53)    (63)    (64)     (74)
                               (322)  (62)    (72)    (73)     (83)
                                      (332)   (333)   (433)    (92)
                                      (2222)  (522)   (532)    (443)
                                              (3222)  (622)    (533)
                                                      (3322)   (632)
                                                      (22222)  (722)
                                                               (3332)
                                                               (5222)
                                                               (32222)
		

Crossrefs

Cf. A001597, A002865, A007916, A052410, A101417, A102430, A108917, A305148, A305630, A305631, A321346, A323093.

Programs

Mathematica

stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
Table[Length[Select[IntegerPartitions[n],And[FreeQ[#,1],stableQ[#,IntegerQ[Log[#1,#2]]&]]&]],{n,30}]