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A325164 Heinz numbers of integer partitions with Durfee square of length 2.

%I A325164 #6 Apr 05 2019 09:29:18
%S A325164 9,15,18,21,25,27,30,33,35,36,39,42,45,49,50,51,54,55,57,60,63,65,66,
%T A325164 69,70,72,75,77,78,81,84,85,87,90,91,93,95,98,99,100,102,105,108,110,
%U A325164 111,114,115,117,119,120,121,123,126,129,130,132,133,135,138,140
%N A325164 Heinz numbers of integer partitions with Durfee square of length 2.
%C A325164 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325164 Also positions of 2 in A257990.
%C A325164 First differs from A105441 in lacking 125.
%C A325164 The Durfee length 1 case is A093641. The enumeration of Durfee length 2 partitions by sum is given by A006918, while that of Durfee length 3 partitions is given by A117485.
%H A325164 Gus Wiseman, <a href="/A325164/a325164.png">Young diagrams corresponding to the first 36 terms.</a>
%e A325164 The sequence of terms together with their prime indices begins:
%e A325164    9: {2,2}
%e A325164   15: {2,3}
%e A325164   18: {1,2,2}
%e A325164   21: {2,4}
%e A325164   25: {3,3}
%e A325164   27: {2,2,2}
%e A325164   30: {1,2,3}
%e A325164   33: {2,5}
%e A325164   35: {3,4}
%e A325164   36: {1,1,2,2}
%e A325164   39: {2,6}
%e A325164   42: {1,2,4}
%e A325164   45: {2,2,3}
%e A325164   49: {4,4}
%e A325164   50: {1,3,3}
%e A325164   51: {2,7}
%e A325164   54: {1,2,2,2}
%e A325164   55: {3,5}
%e A325164   57: {2,8}
%e A325164   60: {1,1,2,3}
%t A325164 durf[n_]:=Length[Select[Range[PrimeOmega[n]],Reverse[Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]][[#]]>=#&]];
%t A325164 Select[Range[100],durf[#]==2&]
%Y A325164 Cf. A006918, A056239, A093641, A112798, A115994, A117485, A252464, A257990, A325163, A325170.
%K A325164 nonn
%O A325164 1,1
%A A325164 _Gus Wiseman_, Apr 05 2019