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 A325283 #6 Apr 17 2019 19:09:13
%S A325283 2,4,6,12,18,20,24,28,40,48,60,84,90,120,126,132,140,150,156,168,180,
%T A325283 198,204,220,228,234,240,252,260,264,270,276,280
%N A325283 Heinz numbers of integer partitions with maximum adjusted frequency depth for partitions of that sum.
%C A325283 The enumeration of these partitions by sum is given by A325254.
%C A325283 The adjusted frequency depth of an integer partition is 0 if the partition is empty, and otherwise it is 1 plus the number of times one must take the multiset of multiplicities to reach a singleton. For example, the partition (32211) has adjusted frequency depth 5 because we have: (32211) -> (221) -> (21) -> (11) -> (2).
%C A325283 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A325283 The sequence of terms together with their prime indices and their omega-sequences (see A323023) begins:
%e A325283 2: {1} (1)
%e A325283 4: {1,1} (2,1)
%e A325283 6: {1,2} (2,2,1)
%e A325283 12: {1,1,2} (3,2,2,1)
%e A325283 18: {1,2,2} (3,2,2,1)
%e A325283 20: {1,1,3} (3,2,2,1)
%e A325283 24: {1,1,1,2} (4,2,2,1)
%e A325283 28: {1,1,4} (3,2,2,1)
%e A325283 40: {1,1,1,3} (4,2,2,1)
%e A325283 48: {1,1,1,1,2} (5,2,2,1)
%e A325283 60: {1,1,2,3} (4,3,2,2,1)
%e A325283 84: {1,1,2,4} (4,3,2,2,1)
%e A325283 90: {1,2,2,3} (4,3,2,2,1)
%e A325283 120: {1,1,1,2,3} (5,3,2,2,1)
%e A325283 126: {1,2,2,4} (4,3,2,2,1)
%e A325283 132: {1,1,2,5} (4,3,2,2,1)
%e A325283 140: {1,1,3,4} (4,3,2,2,1)
%e A325283 150: {1,2,3,3} (4,3,2,2,1)
%e A325283 156: {1,1,2,6} (4,3,2,2,1)
%e A325283 168: {1,1,1,2,4} (5,3,2,2,1)
%e A325283 180: {1,1,2,2,3} (5,3,2,2,1)
%t A325283 nn=30;
%t A325283 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325283 fdadj[ptn_List]:=If[ptn=={},0,Length[NestWhileList[Sort[Length/@Split[#]]&,ptn,Length[#]>1&]]];
%t A325283 mfds=Table[Max@@fdadj/@IntegerPartitions[n],{n,nn}];
%t A325283 Select[Range[Prime[nn]],fdadj[primeMS[#]]==mfds[[Total[primeMS[#]]]]&]
%Y A325283 Cf. A011784, A056239, A112798, A118914, A181819, A182857, A225486, A323014, A323023, A325254, A325258, A325277, A325278, A325282.
%Y A325283 Integer partition triangles: A008284 (first omega), A116608 (second omega), A325242 (third omega), A325268 (second-to-last omega), A225485 or A325280 (length/frequency depth).
%K A325283 nonn,more
%O A325283 1,1
%A A325283 _Gus Wiseman_, Apr 17 2019