This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A323089 #8 Jan 04 2019 17:33:24
%S A323089 1,1,1,2,1,2,3,3,4,4,5,6,7,9,10,12,14,16,20,22,26,31,34,40,46,51,59,
%T A323089 66,75,86,96,110,123,139,157,176,199,221,248,278,309,346,385,427,476,
%U A323089 528,586,650,719,795,880,973,1074,1186,1307,1439,1584,1744,1915,2104
%N A323089 Number of strict integer partitions of n using 1 and numbers that are not perfect powers.
%F A323089 O.g.f.: (1 + x) * Product_{n in A007916} (1 + x^n).
%e A323089 A list of all strict integer partitions using 1 and numbers that are not perfect powers begins:
%e A323089 1: (1) 8: (5,2,1) 12: (12) 14: (14)
%e A323089 2: (2) 9: (7,2) 12: (11,1) 14: (13,1)
%e A323089 3: (3) 9: (6,3) 12: (10,2) 14: (12,2)
%e A323089 3: (2,1) 9: (6,2,1) 12: (7,5) 14: (11,3)
%e A323089 4: (3,1) 9: (5,3,1) 12: (7,3,2) 14: (11,2,1)
%e A323089 5: (5) 10: (10) 12: (6,5,1) 14: (10,3,1)
%e A323089 5: (3,2) 10: (7,3) 12: (6,3,2,1) 14: (7,6,1)
%e A323089 6: (6) 10: (7,2,1) 13: (13) 14: (7,5,2)
%e A323089 6: (5,1) 10: (6,3,1) 13: (12,1) 14: (6,5,3)
%e A323089 6: (3,2,1) 10: (5,3,2) 13: (11,2) 14: (6,5,2,1)
%e A323089 7: (7) 11: (11) 13: (10,3) 15: (15)
%e A323089 7: (6,1) 11: (10,1) 13: (10,2,1) 15: (14,1)
%e A323089 7: (5,2) 11: (7,3,1) 13: (7,6) 15: (13,2)
%e A323089 8: (7,1) 11: (6,5) 13: (7,5,1) 15: (12,3)
%e A323089 8: (6,2) 11: (6,3,2) 13: (7,3,2,1) 15: (12,2,1)
%e A323089 8: (5,3) 11: (5,3,2,1) 13: (6,5,2) 15: (11,3,1)
%t A323089 perpowQ[n_]:=GCD@@FactorInteger[n][[All,2]]>1;
%t A323089 Table[Length[Select[IntegerPartitions[n],UnsameQ@@#&&And@@Not/@perpowQ/@#&]],{n,65}]
%Y A323089 Cf. A001597, A007916, A052410, A087897, A276431, A303707, A305630, A323088, A323090.
%K A323089 nonn
%O A323089 0,4
%A A323089 _Gus Wiseman_, Jan 04 2019