OFFSET
1,1
COMMENTS
The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).
EXAMPLE
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)
MATHEMATICA
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[#]]&]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 25 2018
STATUS
approved