A301988 Nonprime Heinz numbers of integer partitions whose product is equal to their sum.

9, 30, 84, 108, 200, 264, 624, 1120, 1440, 1632, 3648, 7040, 8832, 12544, 16128, 20736, 22272, 33280, 47616, 76800, 113664, 157696, 174080, 202752, 251904, 528384, 778240, 1155072, 1490944, 1916928, 2605056, 3440640, 3768320, 3964928, 4423680, 5799936

Offset

1,1

Comments

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..36.

Example

Sequence of reversed integer partitions begins: (22), (123), (1124), (11222), (11133), (11125), (111126), (1111134), (11111223), (1111127), (11111128), (111111135), (111111129), (1111111144), (11111111224), (111111112222).

Mathematica

primeMS[n_]:=If[n===1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]];
Select[Range[200000], !PrimeQ[#]&&Total[primeMS[#]]===Times@@primeMS[#]&]

Crossrefs

Cf. A001055, A002865, A003963, A056239, A276024, A284640, A296150, A299701, A301957, A301987.

Sequence in context: A273640 A344522 A291919 * A334853 A212517 A319839

Adjacent sequences: A301985 A301986 A301987 * A301989 A301990 A301991

Keyword

nonn

Author

Gus Wiseman, Mar 30 2018

Status

approved