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

1,1

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..55.

Example

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)

Mathematica

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

Crossrefs

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

Sequence in context: A082421 A153798 A368101 * A302590 A316151 A265121

Adjacent sequences: A316089 A316090 A316091 * A316093 A316094 A316095

Keyword

nonn

Author

Gus Wiseman, Jun 24 2018

Status

approved