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