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 A322077 #4 Nov 26 2018 17:04:52
%S A322077 1,1,2,2,3,4,5,5,8,6,7,9,11,10,12,13,15,18,22,15,19,14,30,24,22,21,40,
%T A322077 23,42,29,56,36,27,29,34,47,77,41,39,40
%N A322077 In the ranked poset of integer partitions ordered by refinement, number of integer partitions coarser (greater) than or equal to the integer partition whose multiplicities are the prime indices of n in weakly decreasing order.
%C A322077 This partition (reversed row n of A305936) is generally not the same as the integer partition with Heinz number n. For example, 12 is the Heinz number of (2,1,1), while the integer partition whose multiplicities are (2,1,1) is (3,2,1,1).
%e A322077 The list of a(1) = 1 through a(18) = 18 coarser partitions:
%e A322077 () (1) (2) (3) (3) (4) (4) (6) (6) (5) (5)
%e A322077 (11) (21) (21) (22) (22) (33) (33) (32) (32)
%e A322077 (111) (31) (31) (42) (42) (41) (41)
%e A322077 (211) (211) (51) (51) (221) (221)
%e A322077 (1111) (321) (222) (311) (311)
%e A322077 (321) (2111) (2111)
%e A322077 (411) (11111)
%e A322077 (2211)
%e A322077 .
%e A322077 (7) (6) (6) (7) (10) (7) (9)
%e A322077 (43) (33) (33) (43) (55) (43) (54)
%e A322077 (52) (42) (42) (52) (64) (52) (63)
%e A322077 (61) (51) (51) (61) (73) (61) (72)
%e A322077 (322) (222) (222) (322) (82) (322) (81)
%e A322077 (331) (321) (321) (331) (91) (331) (333)
%e A322077 (421) (411) (411) (421) (433) (421) (432)
%e A322077 (511) (2211) (2211) (511) (442) (511) (441)
%e A322077 (3211) (3111) (3111) (2221) (532) (2221) (522)
%e A322077 (21111) (21111) (3211) (541) (3211) (531)
%e A322077 (111111) (4111) (631) (4111) (621)
%e A322077 (22111) (721) (22111) (711)
%e A322077 (4321) (31111) (3222)
%e A322077 (211111) (3321)
%e A322077 (1111111) (4221)
%e A322077 (4311)
%e A322077 (5211)
%e A322077 (32211)
%t A322077 sps[{}]:={{}};sps[set:{i_,___}]:=Join@@Function[s,Prepend[#,s]&/@sps[Complement[set,s]]]/@Cases[Subsets[set],{i,___}];
%t A322077 mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
%t A322077 nrmptn[n_]:=Join@@MapIndexed[Table[#2[[1]],{#1}]&,If[n==1,{},Flatten[Cases[FactorInteger[n]//Reverse,{p_,k_}:>Table[PrimePi[p],{k}]]]]];
%t A322077 Table[Length[Union[Sort/@Apply[Plus,mps[nrmptn[n]],{2}]]],{n,20}]
%Y A322077 Cf. A063834, A066723, A213427, A265947, A299201, A300383, A317141, A321468, A321472.
%K A322077 nonn,more
%O A322077 1,3
%A A322077 _Gus Wiseman_, Nov 25 2018