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

1,1

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).

Links

Table of n, a(n) for n=1..60.

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[#]]] &]

Crossrefs

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

Sequence in context: A047426 A362781 A323527 * A026487 A130788 A288819

Adjacent sequences: A316088 A316089 A316090 * A316092 A316093 A316094

Keyword

nonn

Author

Gus Wiseman, Jun 24 2018

Status

approved