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A325170 Heinz numbers of integer partitions with origin-to-boundary graph-distance equal to 2.

%I A325170 #9 Jan 08 2021 21:17:21
%S A325170 6,9,10,12,14,15,18,20,21,22,24,25,26,27,28,33,34,35,36,38,39,40,44,
%T A325170 46,48,49,51,52,54,55,56,57,58,62,65,68,69,72,74,76,77,80,81,82,85,86,
%U A325170 87,88,91,92,93,94,95,96,104,106,108,111,112,115,116,118,119
%N A325170 Heinz numbers of integer partitions with origin-to-boundary graph-distance equal to 2.
%C A325170 The origin-to-boundary graph-distance of a Young diagram is the minimum number of unit steps East or South from the upper-left square to a nonsquare in the lower-right quadrant. It is also the side-length of the minimum triangular partition contained inside the diagram.
%C A325170 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%H A325170 Gus Wiseman, <a href="/A325170/a325170.png">Young diagrams corresponding to the first 50 terms.</a>
%e A325170 The sequence of terms together with their prime indices begins:
%e A325170    6: {1,2}
%e A325170    9: {2,2}
%e A325170   10: {1,3}
%e A325170   12: {1,1,2}
%e A325170   14: {1,4}
%e A325170   15: {2,3}
%e A325170   18: {1,2,2}
%e A325170   20: {1,1,3}
%e A325170   21: {2,4}
%e A325170   22: {1,5}
%e A325170   24: {1,1,1,2}
%e A325170   25: {3,3}
%e A325170   26: {1,6}
%e A325170   27: {2,2,2}
%e A325170   28: {1,1,4}
%e A325170   33: {2,5}
%e A325170   34: {1,7}
%e A325170   35: {3,4}
%e A325170   36: {1,1,2,2}
%e A325170   38: {1,8}
%t A325170 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A325170 otb[ptn_]:=Min@@MapIndexed[#1+#2[[1]]-1&,Append[ptn,0]];
%t A325170 Select[Range[200],otb[Reverse[primeMS[#]]]==2&]
%Y A325170 Cf. A001221, A001222, A006918, A056239, A065770, A112798, A174090, A257990, A297113, A325167, A325169.
%K A325170 nonn
%O A325170 1,1
%A A325170 _Gus Wiseman_, Apr 05 2019