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

Author

Gus Wiseman, Mar 30 2018

Keywords

• nonn

Comments

The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k).

Examples

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

Crossrefs

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

Programs

Mathematica

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