A316151 -id:A316151 - cp's OEIS frontend

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

15, 33, 45, 93, 153, 177, 275, 327, 369, 405, 425, 537, 603, 605, 775, 831, 891, 1025, 1059, 1125, 1413, 1445, 1475, 1641, 1705, 1719, 1761, 2057, 2075, 2319, 2511, 2577, 2979, 3175, 3179, 3189, 3459, 3485, 3603, 3609, 3825, 3925, 4299, 4475, 4497, 4565, 4581

Offset: 1

Gus Wiseman, Jun 25 2018

nonn

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

			Sequence of integer partitions of prime numbers into a prime number of prime parts, preceded by their Heinz numbers, begins:
   15: (3,2)
   33: (5,2)
   45: (3,2,2)
   93: (11,2)
  153: (7,2,2)
  177: (17,2)
  275: (5,3,3)
  327: (29,2)
  369: (13,2,2)
  405: (3,2,2,2,2)
  425: (7,3,3)
  537: (41,2)
  603: (19,2,2)
  605: (5,5,3)
  775: (11,3,3)
  831: (59,2)
  891: (5,2,2,2,2)

Cf. A000586, A000607, A038499, A056239, A056768, A064688, A070215, A085755, A302590, A316092, A316151.

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[1000],And[PrimeQ[PrimeOmega[#]],PrimeQ[Total[primeMS[#]]],And@@PrimeQ/@primeMS[#]]&]

cp's OEIS Frontend

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

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