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 A316362 #7 Jun 30 2018 20:40:49 %S A316362 30,105,110,210,238,273,330,385,390,462,506,510,546,570,627,690,714, %T A316362 770,806,858,870,910,930,935,966,1001,1110,1131,1155,1190,1230,1254, %U A316362 1290,1326,1330,1365,1394,1410,1430,1482,1495,1518,1590,1729,1770,1785,1786,1794 %N A316362 Heinz numbers of strict integer partitions such that not every distinct subset has a different average. %C A316362 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). %e A316362 462 is the Heinz number of (5,4,2,1), and the subsets {1,5}, and {2,4} have the same average, so 462 belongs to the sequence. %t A316362 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]]; %t A316362 Select[Range[3000],SquareFreeQ[#]&&!UnsameQ@@Mean/@Union[Subsets[primeMS[#]]]&] %Y A316362 Cf. A032302, A056239, A108917, A122768, A275972, A276024, A296150, A299702, A301899, A316313, A316314, A316361. %K A316362 nonn %O A316362 1,1 %A A316362 _Gus Wiseman_, Jun 30 2018