login
A316091
Heinz numbers of integer partitions of prime numbers.
4
3, 4, 5, 6, 8, 11, 14, 15, 17, 18, 20, 24, 26, 31, 32, 33, 35, 41, 42, 44, 45, 50, 54, 56, 58, 59, 60, 67, 69, 72, 74, 80, 83, 92, 93, 95, 96, 106, 109, 114, 119, 122, 124, 127, 128, 141, 143, 145, 152, 153, 157, 158, 161, 170, 174, 177, 179, 182, 188, 191
OFFSET
1,1
COMMENTS
Also the union of prime-indexed rows of A215366.
The Heinz number of an integer partition (y_1, ..., y_k) is prime(y_1) * ... * prime(y_k).
EXAMPLE
Sequence of all integer partitions of prime numbers begins (2), (1, 1), (3), (2, 1), (1, 1, 1), (5), (4, 1), (3, 2), (7), (2, 2, 1), (3, 1, 1), (2, 1, 1, 1), (6, 1).
MATHEMATICA
primeMS[n_] := If[n == 1, {}, Flatten[Cases[FactorInteger[n], {p_, k_} :> Table[PrimePi[p], {k}]]]]; Select[Range[100], PrimeQ[Total[primeMS[#]]] &]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 24 2018
STATUS
approved