A316091 Heinz numbers of integer partitions of prime numbers.

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

Author

Gus Wiseman, Jun 24 2018

Keywords

• nonn

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).

Examples

			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).
		

Crossrefs

Cf. A000041, A000607, A056239, A056768, A076610, A100118, A112798, A215366, A296150, A300383, A316092.

Programs

Mathematica

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