cp's OEIS Frontend

A316151 Heinz numbers of strict integer partitions of prime numbers into prime parts.

%I A316151 #6 Jun 25 2018 22:51:38
%S A316151 3,5,11,15,17,31,33,41,59,67,83,93,109,127,157,177,179,191,211,241,
%T A316151 277,283,327,331,353,367,401,431,461,509,537,547,563,587,599,617,709,
%U A316151 739,773,797,831,859,877,919,967,991,1031,1059,1063,1087,1153,1171,1201
%N A316151 Heinz numbers of strict integer partitions of prime numbers into prime parts.
%C A316151 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A316151 Sequence of strict integer partitions of prime numbers into prime parts, preceded by their Heinz numbers, begins:
%e A316151    3: (2)
%e A316151    5: (3)
%e A316151   11: (5)
%e A316151   15: (3,2)
%e A316151   17: (7)
%e A316151   31: (11)
%e A316151   33: (5,2)
%e A316151   41: (13)
%e A316151   59: (17)
%e A316151   67: (19)
%e A316151   83: (23)
%e A316151   93: (11,2)
%t A316151 primeMS[n_]:=If[n===1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316151 Select[Range[100],And[SquareFreeQ[#],PrimeQ[Total[primeMS[#]]],And@@PrimeQ/@primeMS[#]]&]
%Y A316151 Cf. A000586, A000607, A038499, A056239, A056768, A064688, A070215, A085755, A302590, A316092.
%K A316151 nonn
%O A316151 1,1
%A A316151 _Gus Wiseman_, Jun 25 2018