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 A329436 #8 Dec 01 2023 23:26:24
%S A329436 0,1,1,2,2,4,3,5,6,8,7,13,10,16,18,22,21,34,29,44,45,56,56,82,78,100,
%T A329436 109,136,137,185,181,231,247,295,317,399,404,490,533,638,669,817,853,
%U A329436 1020,1108,1276,1371,1638,1728,2017,2186,2519,2702,3153,3371,3885
%N A329436 Expansion of Sum_{k>=1} (-1 + Product_{j>=2} (1 + x^(k*j))).
%C A329436 Inverse Moebius transform of A025147.
%C A329436 Number of uniform (constant multiplicity) partitions of n not containing 1, ranked by the odd terms of A072774. - _Gus Wiseman_, Dec 01 2023
%F A329436 G.f.: Sum_{k>=1} A025147(k) * x^k / (1 - x^k).
%F A329436 a(n) = Sum_{d|n} A025147(d).
%e A329436 From _Gus Wiseman_, Dec 01 2023: (Start)
%e A329436 The a(2) = 1 through a(10) = 8 uniform partitions not containing 1:
%e A329436 (2) (3) (4) (5) (6) (7) (8) (9) (10)
%e A329436 (2,2) (3,2) (3,3) (4,3) (4,4) (5,4) (5,5)
%e A329436 (4,2) (5,2) (5,3) (6,3) (6,4)
%e A329436 (2,2,2) (6,2) (7,2) (7,3)
%e A329436 (2,2,2,2) (3,3,3) (8,2)
%e A329436 (4,3,2) (5,3,2)
%e A329436 (3,3,2,2)
%e A329436 (2,2,2,2,2)
%e A329436 (End)
%t A329436 nmax = 56; CoefficientList[Series[Sum[-1 + Product[(1 + x^(k j)), {j, 2, nmax}], {k, 1, nmax}], {x, 0, nmax}], x] // Rest
%t A329436 Table[Length[Select[IntegerPartitions[n], FreeQ[#,1]&&SameQ@@Length/@Split[#]&]], {n,0,30}] (* _Gus Wiseman_, Dec 01 2023 *)
%Y A329436 The strict case is A025147.
%Y A329436 The version allowing 1 is A047966.
%Y A329436 The version requiring 1 is A097986.
%Y A329436 Cf. A023645, A047968, A072774, A096765, A329435, A329436, A367586.
%K A329436 nonn
%O A329436 1,4
%A A329436 _Ilya Gutkovskiy_, Nov 13 2019