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