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%I #5 May 25 2018 18:57:17
%S 1,169,481,507,793,841,845,1157,1183,1369,1443,1469,1521,1849,1963,
%T 2059,2209,2257,2353,2379,2405,2523,2535,2899,3211,3263,3277,3293,
%U 3367,3471,3549,3653,3721,3887,3965,4107,4121,4181,4225,4329,4394,4407,4563,4601,4667
%N Numbers n such that the z-density of the integer partition with Heinz number n is 0.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%C The z-density of a multiset S of positive integers is Sum_{s in S} (omega(s) - 1) - omega(lcm(S)) where omega = A001221 is number of distinct prime factors.
%t zens[n_]:=If[n==1,0,Total@Cases[FactorInteger[n],{p_,k_}:>k*(PrimeNu[PrimePi[p]]-1)]-PrimeNu[LCM@@Cases[FactorInteger[n],{p_,k_}:>PrimePi[p]]]];
%t Select[Range[1000],zens[#]==0&]
%Y Cf. A001221, A030019, A048143, A056239, A112798, A290103, A302242, A303837, A304118, A304714, A304716, A305001, A305052, A305053, A305054.
%K nonn
%O 1,2
%A _Gus Wiseman_, May 24 2018