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A325761 Heinz numbers of integer partitions whose length is itself a part.

%I A325761 #5 May 18 2019 22:46:51
%S A325761 1,2,6,9,15,20,21,30,33,39,45,50,51,56,57,69,70,75,84,87,93,105,110,
%T A325761 111,123,125,126,129,130,140,141,159,165,170,175,176,177,183,189,190,
%U A325761 195,196,201,210,213,219,230,237,245,249,255,264,267,275,285,290,291
%N A325761 Heinz numbers of integer partitions whose length is itself a part.
%C A325761 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C A325761 The enumeration of these partitions by sum is given by A002865.
%e A325761 The sequence of terms together with their prime indices begins:
%e A325761     1: {}
%e A325761     2: {1}
%e A325761     6: {1,2}
%e A325761     9: {2,2}
%e A325761    15: {2,3}
%e A325761    20: {1,1,3}
%e A325761    21: {2,4}
%e A325761    30: {1,2,3}
%e A325761    33: {2,5}
%e A325761    39: {2,6}
%e A325761    45: {2,2,3}
%e A325761    50: {1,3,3}
%e A325761    51: {2,7}
%e A325761    56: {1,1,1,4}
%e A325761    57: {2,8}
%e A325761    69: {2,9}
%e A325761    70: {1,3,4}
%e A325761    75: {2,3,3}
%e A325761    84: {1,1,2,4}
%e A325761    87: {2,10}
%t A325761 Select[Range[100],MemberQ[PrimePi/@First/@FactorInteger[#],PrimeOmega[#]]&]
%Y A325761 Cf. A001222, A002865, A056239, A093641, A109298, A110295, A112798, A118914, A325762, A325763.
%K A325761 nonn
%O A325761 1,2
%A A325761 _Gus Wiseman_, May 18 2019