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A301988
Nonprime Heinz numbers of integer partitions whose product is equal to their sum.
8
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).
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[#]&]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Mar 30 2018
STATUS
approved