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%I #6 Apr 06 2019 09:59:35
%S 27,45,54,63,75,81,90,99,105,108,117,126,135,147,150,153,162,165,171,
%T 180,189,195,198,207,210,216,225,231,234,243,252,255,261,270,273,279,
%U 285,294,297,300,306,315,324,330,333,342,345,351,357,360,363,369,378,387
%N Heinz numbers of integer partitions with at least three parts, the third of which is 2.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C The enumeration of these partitions by sum is given by A006918 (see Emeric Deutsch's comment there).
%e The sequence of terms together with their prime indices begins:
%e 27: {2,2,2}
%e 45: {2,2,3}
%e 54: {1,2,2,2}
%e 63: {2,2,4}
%e 75: {2,3,3}
%e 81: {2,2,2,2}
%e 90: {1,2,2,3}
%e 99: {2,2,5}
%e 105: {2,3,4}
%e 108: {1,1,2,2,2}
%e 117: {2,2,6}
%e 126: {1,2,2,4}
%e 135: {2,2,2,3}
%e 147: {2,4,4}
%e 150: {1,2,3,3}
%e 153: {2,2,7}
%e 162: {1,2,2,2,2}
%e 165: {2,3,5}
%e 171: {2,2,8}
%e 180: {1,1,2,2,3}
%t primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],PrimeOmega[#]>=3&&Reverse[primeMS[#]][[3]]==2&]
%Y Cf. A000726, A002620, A004250, A006918, A056239, A097701, A112798, A257990, A297113, A325164, A325169, A325170.
%K nonn
%O 1,1
%A _Gus Wiseman_, Apr 05 2019
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