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

3, 5, 11, 15, 17, 31, 33, 41, 59, 67, 83, 93, 109, 127, 157, 177, 179, 191, 211, 241, 277, 283, 327, 331, 353, 367, 401, 431, 461, 509, 537, 547, 563, 587, 599, 617, 709, 739, 773, 797, 831, 859, 877, 919, 967, 991, 1031, 1059, 1063, 1087, 1153, 1171, 1201

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..53.

Example

Sequence of strict integer partitions of prime numbers into prime parts, preceded by their Heinz numbers, begins:
   3: (2)
   5: (3)
  11: (5)
  15: (3,2)
  17: (7)
  31: (11)
  33: (5,2)
  41: (13)
  59: (17)
  67: (19)
  83: (23)
  93: (11,2)

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[100], And[SquareFreeQ[#], PrimeQ[Total[primeMS[#]]], And@@PrimeQ/@primeMS[#]]&]

Crossrefs

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

Sequence in context: A368101 A316092 A302590 * A265121 A281575 A105772

Adjacent sequences: A316148 A316149 A316150 * A316152 A316153 A316154

Keyword

nonn

Author

Gus Wiseman, Jun 25 2018

Status

approved