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A316151
Heinz numbers of strict integer partitions of prime numbers into prime parts.
1
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).
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[#]]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 25 2018
STATUS
approved