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%I #5 May 18 2019 22:46:51
%S 1,2,6,9,15,20,21,30,33,39,45,50,51,56,57,69,70,75,84,87,93,105,110,
%T 111,123,125,126,129,130,140,141,159,165,170,175,176,177,183,189,190,
%U 195,196,201,210,213,219,230,237,245,249,255,264,267,275,285,290,291
%N Heinz numbers of integer partitions whose length is itself a part.
%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 A002865.
%e The sequence of terms together with their prime indices begins:
%e 1: {}
%e 2: {1}
%e 6: {1,2}
%e 9: {2,2}
%e 15: {2,3}
%e 20: {1,1,3}
%e 21: {2,4}
%e 30: {1,2,3}
%e 33: {2,5}
%e 39: {2,6}
%e 45: {2,2,3}
%e 50: {1,3,3}
%e 51: {2,7}
%e 56: {1,1,1,4}
%e 57: {2,8}
%e 69: {2,9}
%e 70: {1,3,4}
%e 75: {2,3,3}
%e 84: {1,1,2,4}
%e 87: {2,10}
%t Select[Range[100],MemberQ[PrimePi/@First/@FactorInteger[#],PrimeOmega[#]]&]
%Y Cf. A001222, A002865, A056239, A093641, A109298, A110295, A112798, A118914, A325762, A325763.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 18 2019
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