A316092 Heinz numbers of integer partitions of prime numbers into prime parts.

3, 5, 11, 15, 17, 31, 33, 41, 45, 59, 67, 83, 93, 109, 127, 153, 157, 177, 179, 191, 211, 241, 275, 277, 283, 297, 327, 331, 353, 367, 369, 375, 401, 405, 425, 431, 459, 461, 509, 537, 547, 563, 587, 599, 603, 605, 617, 709, 739, 773, 775, 797, 825, 831, 837

Offset: 1

Author

Gus Wiseman, Jun 24 2018

Keywords

• nonn

Comments

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

Examples

			Sequence of integer partitions of prime numbers into prime parts together with their Heinz numbers begins:
   3: (2)
   5: (3)
  11: (5)
  15: (2,3)
  17: (7)
  31: (11)
  33: (2,5)
  41: (13)
  45: (2,2,3)
		

Crossrefs

Cf. A000041, A000607, A056239, A056768, A076610, A100118, A112798, A215366, A296150, A300383, A316091.

Programs

Mathematica

primeMS[n_]:=If[n==1,{},Flatten[Cases[FactorInteger[n],{p_,k_}:>Table[PrimePi[p],{k}]]]];
Select[Range[900],And[PrimeQ[Total[primeMS[#]]],And@@PrimeQ/@primeMS[#]]&]