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%I #6 Jun 25 2018 22:51:38
%S 3,5,11,15,17,31,33,41,59,67,83,93,109,127,157,177,179,191,211,241,
%T 277,283,327,331,353,367,401,431,461,509,537,547,563,587,599,617,709,
%U 739,773,797,831,859,877,919,967,991,1031,1059,1063,1087,1153,1171,1201
%N Heinz numbers of strict integer partitions of prime numbers into prime parts.
%C The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e Sequence of strict integer partitions of prime numbers into prime parts, preceded by their Heinz numbers, begins:
%e 3: (2)
%e 5: (3)
%e 11: (5)
%e 15: (3,2)
%e 17: (7)
%e 31: (11)
%e 33: (5,2)
%e 41: (13)
%e 59: (17)
%e 67: (19)
%e 83: (23)
%e 93: (11,2)
%t primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t Select[Range[100],And[SquareFreeQ[#],PrimeQ[Total[primeMS[#]]],And@@PrimeQ/@primeMS[#]]&]
%Y Cf. A000586, A000607, A038499, A056239, A056768, A064688, A070215, A085755, A302590, A316092.
%K nonn
%O 1,1
%A _Gus Wiseman_, Jun 25 2018
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