cp's OEIS Frontend

A316153 Heinz numbers of integer partitions of prime numbers into a prime number of prime parts.

%I A316153 #4 Jun 25 2018 22:51:44
%S A316153 15,33,45,93,153,177,275,327,369,405,425,537,603,605,775,831,891,1025,
%T A316153 1059,1125,1413,1445,1475,1641,1705,1719,1761,2057,2075,2319,2511,
%U A316153 2577,2979,3175,3179,3189,3459,3485,3603,3609,3825,3925,4299,4475,4497,4565,4581
%N A316153 Heinz numbers of integer partitions of prime numbers into a prime number of prime parts.
%C A316153 The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
%e A316153 Sequence of integer partitions of prime numbers into a prime number of prime parts, preceded by their Heinz numbers, begins:
%e A316153    15: (3,2)
%e A316153    33: (5,2)
%e A316153    45: (3,2,2)
%e A316153    93: (11,2)
%e A316153   153: (7,2,2)
%e A316153   177: (17,2)
%e A316153   275: (5,3,3)
%e A316153   327: (29,2)
%e A316153   369: (13,2,2)
%e A316153   405: (3,2,2,2,2)
%e A316153   425: (7,3,3)
%e A316153   537: (41,2)
%e A316153   603: (19,2,2)
%e A316153   605: (5,5,3)
%e A316153   775: (11,3,3)
%e A316153   831: (59,2)
%e A316153   891: (5,2,2,2,2)
%t A316153 primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
%t A316153 Select[Range[1000],And[PrimeQ[PrimeOmega[#]],PrimeQ[Total[primeMS[#]]],And@@PrimeQ/@primeMS[#]]&]
%Y A316153 Cf. A000586, A000607, A038499, A056239, A056768, A064688, A070215, A085755, A302590, A316092, A316151.
%K A316153 nonn
%O A316153 1,1
%A A316153 _Gus Wiseman_, Jun 25 2018