cp's OEIS Frontend

A323054 Number of strict integer partitions of n with no 1's such that no part is a power of any other part.

%I A323054 #12 Dec 30 2020 03:39:58
%S A323054 1,0,1,1,1,2,1,3,3,4,4,6,6,8,9,12,13,16,19,21,25,30,36,40,47,53,63,71,
%T A323054 83,94,107,121,140,159,180,204,233,260,296,334,377,421,474,532,598,
%U A323054 668,750,835,933,1038,1163,1292,1435,1597,1771,1966,2180,2421,2673
%N A323054 Number of strict integer partitions of n with no 1's such that no part is a power of any other part.
%H A323054 Fausto A. C. Cariboni, <a href="/A323054/b323054.txt">Table of n, a(n) for n = 0..350</a>
%e A323054 The a(2) = 1 through a(13) = 8 strict integer partitions (A = 10, B = 11, C = 12, D = 13):
%e A323054   (2)  (3)  (4)  (5)   (6)  (7)   (8)   (9)   (A)    (B)    (C)    (D)
%e A323054                  (32)       (43)  (53)  (54)  (64)   (65)   (75)   (76)
%e A323054                             (52)  (62)  (63)  (73)   (74)   (84)   (85)
%e A323054                                         (72)  (532)  (83)   (A2)   (94)
%e A323054                                                      (92)   (543)  (A3)
%e A323054                                                      (632)  (732)  (B2)
%e A323054                                                                    (643)
%e A323054                                                                    (652)
%t A323054 stableQ[u_,Q_]:=!Apply[Or,Outer[#1=!=#2&&Q[#1,#2]&,u,u,1],{0,1}];
%t A323054 Table[Length[Select[IntegerPartitions[n],And[FreeQ[#,1],UnsameQ@@#,stableQ[#,IntegerQ[Log[#1,#2]]&]]&]],{n,30}]
%Y A323054 Cf. A001597, A007916, A025147, A052410, A078374, A087897, A120641, A275972, A303362, A323053, A323087, A323088.
%K A323054 nonn
%O A323054 0,6
%A A323054 _Gus Wiseman_, Jan 04 2019