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 A130689 #25 Apr 26 2021 21:26:45
%S A130689 1,1,2,3,5,6,10,11,16,19,26,28,41,43,56,65,82,88,115,122,155,174,209,
%T A130689 225,283,305,363,402,477,514,622,666,783,858,990,1078,1268,1362,1561,
%U A130689 1708,1958,2111,2433,2613,2976,3247,3652,3938,4482,4821,5422
%N A130689 Number of partitions of n such that every part divides the largest part; a(0) = 1.
%C A130689 First differs from A130714 at a(11) = 28, A130714(11) = 27. - _Gus Wiseman_, Apr 23 2021
%H A130689 Alois P. Heinz, <a href="/A130689/b130689.txt">Table of n, a(n) for n = 0..5000</a> (first 1001 terms from Andrew Howroyd)
%F A130689 G.f.: 1 + Sum_{n>0} x^n/Product_{d divides n} (1-x^d).
%e A130689 For n = 6 we have 10 such partitions: [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 2], [1, 1, 2, 2], [2, 2, 2], [1, 1, 1, 3], [3, 3], [1, 1, 4], [2, 4], [1, 5], [6].
%e A130689 From _Gus Wiseman_, Apr 18 2021: (Start)
%e A130689 The a(1) = 1 through a(8) = 16 partitions:
%e A130689 (1) (2) (3) (4) (5) (6) (7) (8)
%e A130689 (11) (21) (22) (41) (33) (61) (44)
%e A130689 (111) (31) (221) (42) (331) (62)
%e A130689 (211) (311) (51) (421) (71)
%e A130689 (1111) (2111) (222) (511) (422)
%e A130689 (11111) (411) (2221) (611)
%e A130689 (2211) (4111) (2222)
%e A130689 (3111) (22111) (3311)
%e A130689 (21111) (31111) (4211)
%e A130689 (111111) (211111) (5111)
%e A130689 (1111111) (22211)
%e A130689 (41111)
%e A130689 (221111)
%e A130689 (311111)
%e A130689 (2111111)
%e A130689 (11111111)
%e A130689 (End)
%t A130689 Table[If[n==0,1,Length[Select[IntegerPartitions[n],FreeQ[#,1]&&And@@IntegerQ/@(Max@@#/#)&]]],{n,0,30}] (* _Gus Wiseman_, Apr 18 2021 *)
%o A130689 (PARI) seq(n)={Vec(1 + sum(m=1, n, my(u=divisors(m)); x^m/prod(i=1, #u, 1 - x^u[i] + O(x^(n-m+1)))))} \\ _Andrew Howroyd_, Apr 17 2021
%Y A130689 Cf. A018818, A117086.
%Y A130689 The dual version is A083710.
%Y A130689 The case without 1's is A339619.
%Y A130689 The Heinz numbers of these partitions are the complement of A343337.
%Y A130689 The complement is counted by A343341.
%Y A130689 The strict case is A343347.
%Y A130689 The complement in the strict case is counted by A343377.
%Y A130689 A000009 counts strict partitions.
%Y A130689 A000041 counts partitions.
%Y A130689 A000070 counts partitions with a selected part.
%Y A130689 A006128 counts partitions with a selected position.
%Y A130689 A015723 counts strict partitions with a selected part.
%Y A130689 A072233 counts partitions by sum and greatest part.
%Y A130689 Cf. A066186, A083711, A097986, A338470, A341450, A343346, A343382.
%K A130689 easy,nonn
%O A130689 0,3
%A A130689 _Vladeta Jovovic_, Jul 01 2007